CAIRO (CNN) -- Protests over an anti-Muslim film bled into a third day Thursday near the U.S. Embassy in Cairo, as U.S. President Barack Obama warned in a television interview that it would be "a real big problem" if Egypt fails to protect American interests in the country.
Some of the demonstrators threw rocks and Molotov cocktails. Police tried to disperse them by firing tear gas canisters from police vehicles as they drove through Tahrir Square, near the embassy.
The protest turned violent as demonstrators threw rocks and pushed through barbed wire fencing outside the embassy, according to Alla Mahmoud, a spokesman for the Egyptian Interior Ministry. Two police trucks and a car were set on fire.
"Forces were able to push them down toward Tahrir Square farther from embassy street," Mahmoud said, adding that some arrests had been made.
By early Thursday, protesters had been pushed 100 yards from the embassy, said journalist Ian Lee in Cairo.
At least 13 protesters and six police officers were injured, Egyptian government officials said Thursday.
The clashes came amid heightened tensions at U.S. diplomatic missions in the region following Tuesday's attack on the U.S. Consulate in Benghazi, Libya, that left Ambassador Chris Stevens and three other consular officials dead.
That same day, the 11th anniversary of the 9/11 terrorist attacks, several men scaled the walls of the U.S. Embassy in Cairo and tore down its U.S. flag.
The protests follow the online release of a film produced in the United States that denigrates Prophet Mohammed.
Obama, in an interview Wednesday with Telemundo, said Egypt is neither an ally nor an enemy of the United States. He said how the country responds to the incident will play a role in the future relationship between United States and Egypt -- which ranked fifth among nations receiving U.S. foreign aid in 2010, according to U.S. Agency for International Development statistics.
"I don't think that we would consider them an ally, but we don't consider them an enemy," Obama told Telemundo. "They're a new government that is trying to find its way. They were democratically elected. I think that we are going to have to see how they respond to this incident."
Obama said that if Egypt takes actions that "indicate they're not taking responsibilities, as all other countries do where we have embassies, I think that's going to be a real big problem."
On Tuesday, police and Egyptian troops formed defensive lines around the U.S. Embassy to prevent demonstrators from advancing, but not before the protesters placed a black flag atop a ladder in the American compound. Police arrested four protesters, but the failure of Egyptian authorities to take action sooner has been widely questioned.
In the initial aftermath of the attack, Egyptian President Mohamed Morsy focused his comments mostly on the film, condemning those who produced it as violating Islamic strictures against defaming Mohammed.
"The presidency condemns in the strongest terms the attempt of a group to insult the place of the Messenger, the Prophet Mohammed ... and condemns the people who have produced this radical work," the president said in a statement posted on his Facebook page. "The Egyptian people, both Muslims and Christians, refuse such insults on sanctities."
On Thursday, he reiterated his concern over the film in a telephone call with Obama, but also condemned the embassy attacks.
"Those who are attacking the embassies do not represent any of us," he said in comments from Brussels, Belgium, where he was visiting the headquarters of the European Union.
The protests, and Obama's comments, come during a delicate period in the relationship between the United States and Egypt under Morsy, the country's first leader since the overthrow last year of longtime ruler Hosni Mubarak -- a key Western ally.
Obama spoke with Morsy on Wednesday "to review the strategic partnership between the United States and Egypt, and our ongoing efforts to strengthen bilateral economic and security cooperation," the White House said in a statement early Thursday.
During the call, the statement said, Obama told Morsy that "he rejects efforts to denigrate Islam, but underscored that there is never any justification for violence against innocents and acts that endanger American personnel and facilities."
Morsy "expressed his condolences for the tragic loss of American life in Libya and emphasized that Egypt would honor its obligation to ensure the safety of American personnel," according to the White House statement.
The Cairo incident was not nearly as bad as the violence in neighboring Libya, where an attack on the U.S. Consulate in Benghazi killed four Americans, including Stevens. A pro-al Qaeda group was to blame for that attack, according to sources tracking militant groups in the region.
In a statement posted to his Facebook page, Morsy called on Egyptian diplomats in Washington "to take legal action against those people who seek to ruin relationships and discussions between people and countries."