NBC's Chuck Todd report.
Updated 6:22 p.m. ET: CHICAGO -- President Barack Obama on Sunday pressed world leaders to help implement a strategy for post-2014 Afghanistan after U.S. troops leave, a transition that Afghan President Hamid Karzai said will mark the day that his war-torn country is "no longer a burden" on the rest of the world.
Obama and Karzai met on the sidelines of the NATO summit on Sunday to discuss Afghanistan's post-conflict future. After the meeting, Obama told reporters that the two-day summit would focus on Afghanistan's move to peace and stability after a decade of war.
"We still have a lot of work to do and there will be great challenges ahead," Obama said. "The loss of life continues in Afghanistan and there will be hard days ahead."
Standing next to Obama, Karzai reaffirmed his commitment to the transition timetable process, which he said will lead to a time when Afghanistan "is no longer a burden on the shoulder of our friends in the international community, on the shoulders of the United States and other allies."
Karzai also thanked Americans for the help that their "taxpayer money" has done in Afghanistan.
Pablo Martinez Monsivais / AP
President Barack Obama, right, shakes hands with with Afghan President Hamid Karzai during their meeting at the NATO summit in Chicago on Sunday.
"Afghanistan is fully aware of the task ahead and of what Afghanistan needs to do to reach the objectives that we all have of a stable, peaceful and self-reliant Afghanistan," he said.
President Barack Obama welcomes foreign leaders to the NATO summit in Chicago. NBC's Kristen Welker reports.
Obama later opened the summit by telling world leaders: "For over 65 years our alliance has been the bedrock of our common security, our freedom and our prosperty, and although times have changed the reasons for our alliance has not."
Obama urged NATO leaders to ratify a "broad consensus" for gradually turning over security to Afghan forces and pulling out most of the 130,000 NATO troops by the end of 2014.
Earlier, a top NATO official insisted that the Afghanistan fighting coalition will remain whole despite France's plans to yank combat troops out early.
"There will be no rush for the exits," NATO Secretary General Anders Fogh Rasmussen said. "We will stay committed and see it through to a successful end. Our goal, our strategy, our timetable remain unchanged."
NATO leaders gathered in Chicago to chart a path out of Afghanistan as war-weary Western nations seek to fend off dissent in their alliance and ensure Afghanistan can hold a still-potent Taliban at bay when foreign troops withdraw.
Obama was hosting the two-day summit in his hometown, a day after leaders of major industrialized nations tackled Europe's debt crisis, backing keeping Greece in the euro zone and vowing to take steps necessary to revitalize the world economy.
Public opinion in Europe and the United States is solidly against the war, with a majority of Americans now saying it is unwinnable or not worth continuing.
Newly elected French President Francois Hollande has said he will withdraw all French combat troops from Afghanistan by year's end — a full two years before the timeline agreed to by nations in the U.S.-led NATO coalition.
"President Hollande has stated that France would be prepared to support Afghanistan in a different way," Rasmussen said.
But signaling tensions over the issue, German Chancellor Angela Merkel told reporters: "We went into Afghanistan together, we want to leave Afghanistan together."
Hollande repeated a pledge during his inaugural visit to Washington last week to pull "combat troops" from Afghanistan this year. He has said an extremely limited number of soldiers would remain to train Afghan forces and bring back equipment beyond 2012.
"This decision is an act of sovereignty and must be done in good coordination with our allies and partners," said Hollande, who was to discuss his exit plans with Karzai.
A last-minute addition to the list of leaders at the NATO meeting was President Asif Ali Zardari of Pakistan, whose western tribal areas provide shelter to militants attacking Karzai's government and NATO forces. He pressed the United States to help find a "permanent solution'' to U.S. drone strikes that have fueled tensions between the two uneasy allies.
"The president said that Pakistan wanted to find a permanent solution to the drone issue as it not only violated our sovereignty but also inflamed public sentiments,'' Zardari spokesman Farhatullah Babar said in a statement after the Pakistani leader met with U.S. Secretary of State Hillary Clinton on the sidelines of the summit.
The statement did not specify what such a solution might entail.
Gen. John Allen, the U.S. commander in Afghanistan, told Reuters he was confident a deal would eventually be struck but "whether it's in days or weeks, I don't know."
Zardari also called for the United States to do more to make amends for the deaths of 24 Pakistani soldiers killed in November by U.S. aircraft along the border with Afghanistan.
Pakistan has demanded a high-level apology for that incident, which the White House has resisted so far.
Fiscal demands, including plans for major cuts to defense spending in Europe and the United States, were sure to color the talks in Chicago, as they did those between G-8 leaders.
The overarching message from that G-8 summit reflected Obama's own concerns that euro-zone contagion, which threatens the future of Europe's 17-country single currency bloc, could hurt a fragile U.S. recovery and his re-election chances.
Information from The Associated Press and Reuters is included in this report.
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