(CNN) -- Villagers in northern Syria picked pieces of a downed fighter jet from an olive grove Wednesday after rebel fighters claimed to have shot down three government aircraft in 24 hours.
Syrian President Bashar al-Assad's government has relied more on air power to battle the 21-month-old revolt against it, and witnesses said a cheer went up when the jet went down near Aleppo.
"We want to take this ... to show them in the other villages," a man who identified himself as Abu Dargham told CNN as he showed off two twisted chunks of metal. "Let them see what happened to these planes."
The downed plane's tail was largely intact, but the fuselage was in pieces and the type of aircraft was not immediately identifiable. Locals picked it apart, with some stuffing pieces into in bags as a tractor hauled away what appeared to be an engine. Cheering children were piled on the tractor as it drove away.
Witnesses said two fliers ejected from the plane before the crash. One was found unconscious and taken to a makeshift clinic, while villagers said they were still searching for the other late Wednesday.
Syrian men inspect the scene of a car bomb explosion on Wednesday, November 28, in Jaramana, a small town near Damascus that has provided a refuge for pro-government Syrians displaced in the civil war. Twin car bombs near the capital killed dozens, state media reported. View photos from November 2012 in this gallery, and see October 2012 photos from the conflict here.
Syrian men walk around a pool of blood at the site of a car bomb explosion in Jaramana on Wednesday. Syrian rebels celebrate on top of the remains of a Syrian government fighter jet that was shot down at Daret Ezza, on the border between the provinces of Idlib and Aleppo, on Wednesday. The scars of war -- damage is readily visible at a government-controlled building in al-Layramun district of Aleppo on Monday, November 26.
A man stands next to a crater in the village of Atme after a Syrian warplane launched an attack against a rebel command center near the border with Turkey on Monday.
A Syrian man cooks a meal at a refugee camp in Qah, near the northwestern city of Idlib on Saturday, November 24. Syrian boys from Ras al-Ain attempt to cross back into Syria at the Turkish border town of Ceylanpinar on Saturday. Syrian rebels and bystanders watch as a bulldozer removes debris from outside the Dar Al-Shifa hospital in Aleppo on Thursday, November 22.
Rescue workers cover a corpse under the debris outside Dar Al-Shifa hospital in Aleppo on Thursday.
A Syrian boy cleans debris from outside Dar Al-Shifa hospital in Aleppo on Thursday.
Syrian refugees fleeing their homes in the northern Syrian town of Ras al-Ain walk to cross the border fence into Turkey, as seen from the Turkish border town of Ceylanpinar, on Wednesday, November 21.
Syrian rebel fighters drive through the gate of Syrian Government Army Base 46 after its capture, near Aleppo on Wednesday. Defected Gen. Mohammed Ahmed al-Faj, who commanded the assault, hailed the capture of the base as "one of our biggest victories since the start of the revolution" against President Bashar al-Assad.
Smoke and fire rise from the Roman citadel of Kalat al-Numan after it was bombed by a Syrian government jet on Tuesday, November 20, in Maaret al-Numan, Syria. The Roman-era town of 150,000 is now virtually deserted due to the heavy shelling and aerial bombardments.
Syrians ride on a horse-drawn cart in the streets of the Tarik al-Bab neighborhood in Aleppo on Sunday, November 18.
Syrian rebels stand guard outside a church in the town of Ras al-Ain near the border with Turkey on Friday, November 16. A picture shows a heavily damaged house after airstrikes by Syrian regime forces in Ras al-Ain on Friday.
A Syrian rebel takes cover during fighting against government forces in Aleppo on Thursday, November 15.
A Turkish soldier in a foxhole in Ceylanpinar, Turkey, watches Syrian opposition fighters praying in the strategic Syrian border town of Ras al-Ain on Wednesday, November 14.
A Syrian rebel commander of the Halab al-Shabah battalion motivates fighters during clashes with regime forces in Al-Amariya district of Aleppo on Tuesday, November 13.
Smoke billows from burning tires as a Syrian rebel fires toward regime forces in Aleppo on Tuesday.
Syrian rebels take position in Aleppo on Tuesday.
Smoke rises after Syrian aircraft bombed the strategic border town of Ras al-Ain, killing at least four people, wounding many others and sending panicked residents fleeing across to Turkey on Monday, November 12.
Syrian opposition fighter Bazel Araj, 19, sleeps next to his gun in Aleppo on Sunday, November 11.
Syrian opposition fighters pass a civilian as they patrol the northern city of Aleppo on Sunday.
A Syrian opposition fighter walks in a destroyed house after hard clashes with Syrian regime forces in Ras al Ain on Saturday, November 10.
Syrian nationals cross the border between the Syrian town of Ras al Ain and Ceylanpinar, Turkey, on Saturday.
Syrian army soldiers ride along a street Saturday in the northern province of Aleppo.
A Syrian opposition fighter stands in a destroyed house in Ras al Ain on Saturday.
Syrians cross the border into Turkey on Friday, November 9, near the Turkish town of Ceylanpinar. Smoke rises after an explosion in the Syrian village of Bariqa near the the cease-fire line in the Israeli-controlled Golan Heights on Wednesday, November 7. Israel is asking the U.N. Security Council to address an intrusion by Syrian tanks into the buffer zone between Syria and Israel in the Golan Heights, which Israel says violates the two countries' Separation of Forces agreement.
A picture released by the Syrian Arab News Agency shows damage caused by a mortar attack in a residential district of Damascus, Syria, on Wednesday.
A damaged vehicle and building are damaged after bomb explosions in in Damascus on Wednesday in this photo released by Syria's national news agency, SANA. Multiple bomb explosions on Wednesday hit a hilltop district in Damascus populated by members of Syrian President Bashar al-Assad's Alawite sect, witnesses said. An Israeli Merkava tank crew sits in the Israeli-controlled Golan Heights overlooking the Syrian village of Breqa on Tuesday, November 6. An Israeli military vehicle in the Golan Heights was hit by gunfire from Syria on Monday, the Israeli army said. A mortar shell explodes in the Syrian village of Breqa on Tuesday.
Syrian rescue workers evacuate a woman and her two children from a building targeted by an airstrike from government forces in a town northeast of Aleppo on Sunday, November 4. An AFP correspondent reported three air strikes on the town in close succession.
Syrian people take cover as a second bomb explodes during a rescue attempt in nearby a building that was hit during an air raid by government forces earlier on Sunday.
A Syrian rebel fighter rests on a couch in a rebel-controlled building on the front line in Aleppo's northern Izaa quarter on Sunday.
A mannequin used by rebel fighters as a decoy is seen in an area where clashes continue with pro-government forces in Aleppo on Friday, November 2.
A member of the Free Syrian Army runs for cover from sniper fire in Aleppo on Friday.
Members of the Free Syrian Army stand close to an unexploded bomb dropped by a fighter jet weeks earlier, at a checkpoint in Aleppo on Thursday, November 1.
Buildings lie destoryed by what activists say were missiles fired by a Syrian Air Force fighter jet loyal to Syrian President Bashar al-Assad, in Erbeen, near Damascus on Thursday. See photographs from October.
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Rebels make gains in Syria Rebels posted two videos online to support their claims. One shows rebels carrying an unconscious man wearing what looks like a military pilot uniform, while another includes footage of medics bandaging a bloodied and moaning pilot.
"Here is the pilot who was shelling houses of civilians!" someone says off-camera. "The heroes of Darret Ezza shot down his plane!"
In addition to the jet brought down Wednesday, the rebels say they have shot down two helicopters since Tuesday night. Rebel video showed one helicopter exploding in midair, but CNN could not independently confirm the authenticity of the footage.
The claims of success follow the capture of a key Syrian air force installation last week. Rebel fighters who overran the base reported finding more than 300 Soviet-era anti-aircraft missiles, along with heavy machine guns, rockets and even tanks.
About half the shoulder-fired missiles were inoperable, but the rebels soon posted video instructing viewers how to handle the ones that worked. Syrian commanders often kept the trigger components separately to prevent the weapons from being used if they were captured.
The installation housed troops from the Syrian army's 46th Regiment. Rebel forces surrounded the base for two months, harassing the troops inside with sniper fire and waiting for them to weaken, Hussein al-Shule said.
"The government will try to airdrop supplies from helicopter. They did not dare land," al-Shule said. "Most times they would miss, and we would take the food. It was inedible."
Opposition says 157 killed Wednesday
The claims came on a day when opposition activists said another 160 people were killed in the country's civil war, which dates back to March 2011. Of those, 96 were killed in the Damascus area, most of them in a single incident -- a pair of car bombings in the town of Jaramana that killed 77 people, according to the Local Coordination Committees of Syria, a network of opposition activists.
Jaramana, a small town surrounded by fields, has provided a refuge for pro-government Syrians displaced in the civil war. Its residents are a mix of Christians and Druze, the latter a minority offshoot of Shiite Islam. Women and children were among those killed there, the London-based Syrian Observatory for Human Rights reported.
Syria's Interior Ministry had conflicting numbers for the bombings, reporting 34 dead and 83 injured.
Read more: Opposition says shelling killed 10 children in Syria
At the same time the car bombs went off, two explosive devices simultaneously detonated in the al-Nahda and al-Qerayyat neighborhoods, both of which are in the Damascus suburbs. Officials did not provide a casualty count in those areas.
Government officials blamed the attacks on terrorists, a term Syria routinely uses for rebel fighters and extremist elements in the country.
Read more: Young Syrian amputee makes dangerous journey to find help
About 40,000 civilians have been killed since the first protests began against al-Assad's government, according to the opposition Center for Documentation of Violations in Syria. More than 380,000 Syrian refugees have fled to neighboring countries, creating humanitarian challenges abroad.
CNN cannot confirm claims by the government or the opposition because of government restrictions that prevent journalists from reporting freely within Syria.
Turkey asked NATO Wednesday for Patriot missiles to bolster its air defenses against its southern neighbor, with which it shares an 822-kilometer (about 511-mile) border.
A letter to NATO included the "formal request" that the alliance send "air defense elements," according to a Turkish government statement that cited "the threats and risks posed by the continuing crisis in Syria to our national security."
The statement added that the NATO Council would convene "shortly" to consider the matter.
NATO Secretary-General Anders Fogh Rasmussen said in a Twitter post that the request would be considered without delay. A fact-finding team is on the ground in Turkey, according to Lt. Col. Jay Janzen, a spokesman for Supreme Headquarters Allied Powers Europe.
"The fact-finding teams include experts from the nations that have shown their willingness to offer Patriots as well as Turkish officials and a few NATO experts," he said.
Turkish officials have emphasized that any deployment of the Patriot missiles would be purely for defensive measures. President Abdullah Gul said earlier this month that Turkey has no intention of going to war with Syria.
A NATO official who is not authorized to speak on record to the media told CNN that the fact-finding team now in Turkey includes military personnel from Germany, the United States and Holland, the three countries that have available Patriot missile batteries.
The official also indicated that those batteries could be deployed dozens of kilometers away from the border fence.
"No decisions have been made about the location and numbers of Patriot batteries in Turkey," the official said.
The official said he doesn't believe "there will be an imminent threat from this deployment escalating the conflict between Turkey and Syria."
"By contrast, I think it will demonstrate a deterrence effect," the official said, "and make it clear that NATO is prepared to defend Turkish territory and Turkish population."
CNN's Ivan Watson and Saad Abedine and Ashley Fantz contributed to this report.