Chicago (CNN) -- NATO leaders signed off Monday on President Barack Obama's exit strategy from Afghanistan that calls for an end to combat operations next year and the withdrawal of the U.S.-led international military force by the end of 2014.
Secretary General Anders Fogh Rasmussen told reporters at the conclusion of a two-day summit of the alliance leaders that the plan calls for handing over security responsibilities to Afghan forces in 2013, then withdrawing foreign forces the following year.
After that, a new and different NATO mission will advise, train and assist the expected 350,000-strong Afghanistan force, Rasmussen said.
The second day of their two-day summit focused on Afghanistan, with Afghan President Hamid Karzai and the heads of other countries contributing to the U.S.-led International Security Assistance Force also in attendance.
Obama wanted NATO to commit to long-range support for Afghanistan, and Rasmussen said the alliance would support Afghan forces after the combat mission ends.
"Today we reaffirmed our strong commitment to support their training, equipping, financing and capability development in the years to come," Rasmussen said, adding it will be a "new mission with a new role for NATO," not "ISAF with a different name."
Rasmussen confirmed that some NATO members have agreed to contribute money for the $4 billion a year needed to help fund the Afghanistan security forces after the NATO mission ends, but said the summit was never intended to secure that funding.
While the Afghanistan force is expected to number 350,000 in 2014, Rasmussen said the size would likely decrease in future years depending on the security situation on the ground and other factors.
He also said he expected an agreement soon for Pakistan to reopen its border with Afghanistan to military shipments of departing NATO forces, which would resolve a sticky issue in planning the withdrawal of foreign forces.
"So far, the closure of the transit routes has not had a major impact on our operations," Rasmussen said, but added the transit routes were very important and that he expected their reopening "in the very near future."
Pakistan closed the ground routes after a NATO airstrike in November killed two dozen of its soldiers. NATO insists the incident was an accident. Obama offered his condolences but refused to apologize.
The United States and Pakistan have not come to an agreement on the price of opening the supply lines, according to senior administration officials, who spoke on condition of anonymity because of the sensitivity of the issue.
Without a deal, the officials said Obama would not meet with President Asif Ali Zardari at the summit.
The two were scheduled to hold trilateral talks with Karzai on political reconciliation in Afghanistan. Pakistan's support in reaching a deal with the Taliban is seen as critical in ending the war in Afghanistan.
When asked about turning over security responsibility to Afghan forces next year, Rasmussen denied it was an acceleration of the transition, saying the plan all along was to withdraw troops in 2014 after shifting the lead security role to Afghan forces.
"It has been within our road map right from the outset," he said.
Protesters conducted more peaceful demonstrations such as sit-ins Monday after clashes with police on Sunday, the first day of the summit.
Earlier Monday, Obama told the dozens of heads of state in attendance that the goal is to "responsibly bring this war to an end" in the next 19 months.
He cited a recent strategic partnership agreement he signed with Karzai as a step toward ensuring that "as Afghans stand up, they will not stand alone."
Obama made clear Sunday as the summit opened that he expects the NATO nations and their strategic partners to agree to the withdrawal plan, while assuring Karzai that the 28-nation NATO would not abandon the country.
"Just as we have sacrificed together for our common security, we will stand together united in our determination to complete this mission," Obama said at the start of the summit .
Obama and Karzai, who met a day ahead of Monday's NATO talks on Afghanistan, both agreed that the end of the war was close.
Following their meeting, Obama said the transition of the NATO-led force from a combat role to one of support of Afghan forces paints "a vision post-2014 in which we have ended our combat role, the Afghan war as we understand it is over."
Karzai reiterated his commitment to the timetable, "so that Afghanistan is no longer a burden on the shoulder of our friends in the international community, on the shoulders of the United States and our other allies.
"Afghanistan, indeed, Mr. President, as you very rightly put it, is looking forward to an end to this war, and a transformational decade," he said.
Under Obama's plan, reminiscent of the Iraq withdrawal, security for Afghanistan would transition to Afghan forces by the middle of next year. NATO troops would then remain in training and advisory role to help beef up Afghan forces until their withdrawal at the end of 2014, followed by the new mission to train, advise and assist the Afghan forces.
A small contingent of British forces could remain after NATO forces leave in 2014, a senior British official said. A senior U.S. official said the United Kingdom may keep some troops in Afghanistan post-2014 for counterterrorism purposes. Both officials requested anonymity because they were not authorized to speak to the media.
"I don't want to understate the challenge that we have ahead of us. The Taliban is a resilient and capable opponent," Marine Gen. John Allen, commander of ISAF troops, said Sunday.
"We fully expect that combat is going to continue" as troops are gradually withdrawn over the next 2 ½ years."
As expected, France's new president, Francois Hollande, announced the withdrawal of French combat troops from Afghanistan by year's end. As part of ISAF, French trainers will remain.
A Taliban spokesman called on NATO nations to follow France's lead.
"We call upon all the other NATO member countries to avoid working for the political interests of American officials and answer the call of your own people by immediately removing all your troops from Afghanistan," Taliban spokesman Zabiullah Mujahid said in a statement.
CNN's Chelsea J. Carter, Adam Levine and Tom Cohen contributed to this report.