Afghanistan's Karzai thanks Obama for ?your taxpayers? money?

President Obama, right, during his meeting with Afghan President Hamid Karzai at the NATO Summit in Chicago, May??

Looking to a day when "the Afghan war as we understand it is over," President?Barack Obama met Sunday with Afghan President Hamid Karzai to discuss NATO's withdrawal from that strife-torn country by the end of 2014.

Obama, who has put the draw-down of combat troops at the heart of his foreign policy, declared that "the world is behind the strategy" of giving Afghans control over their own security, but stressed that "now it's our task to implement if effectively."

Karzai, who aims to secure billions of dollars in long-term aid for his country's military and economy, said he looked forward to a day when "Afghanistan is no longer a burden on the shoulders of of our friends in the international community, on the shoulders of the United States and our other allies."

"I'm bringing to you and to the people of the United States the gratitude of the Afghan people for the support that your taxpayers' money has provided Afghanistan over the past decade and for the difference that it has made to the well-being of the Afghan people," Karzai told Obama.

The two leaders met on the sidelines of a high-stakes NATO summit consumed by the question of the alliance's withdrawal from Afghanistan by the end of 2014, and its role beyond that date. ?Obama has made it known he wants leaders gathered here to sign off on a plan to hand over combat duties to Afghan forces in 2013.

"There will be no rush for the exits," NATO Secretary General Anders Fogh Rasmussen told reporters as the summit opened, saying the alliance's plan was sound and vowing to "see it through to a successful end."

Beyond the tight security cordon around the summit, in the streets of Obama's adoptive hometown, protestors denounced the gathering for a second straight day."I would expect that such demonstrations would take place in a peaceful manner," said Rasmussen.

Obama also wanted NATO leaders to flesh out their own commitments to Afghanistan ? both in terms of troops and money ? until 2014 and beyond. Specific dollar amounts are not expected in Chicago, but a July donors conference in Tokyo should spell those out. The price tag for Afghan forces after 2014 is estimated to be $4.1 billion per year. Afghanistan is expected to pay $500 million of that. Karzai has said his country will need at least $10 billion per year in overall aid through 2025.

Obama looked ahead to a future?"in which we have ended our combat role, the Afghan war as we understand it is over, but our commitment to friendship and partnership with Afghanistan continues" and evoked ?"a shared vision that we have in which Afghanistan is able to transition from decades of war to a transformational decade of peace and stability and development."

Obama underlined "the enormous sacrifices that have been made by the American people, most profoundly by American troops, as well as the troops of our other coalition partners" and said Americans "recognize the hardship that the Afghan people have been through."

"The loss of life continues in Afghanistan. There will be hard days ahead. But we're confident that we're on the right track," he said.

"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. In the meantime, until then, thank you for your support," Karzai said.

(Karzai had given a somewhat different assessment of Kabul's relationship with Washington at a December 2008 joint press conference with then-President George W. Bush.

"Afghanistan will not allow the international community leave it before we are fully on our feet, before we are strong enough to defend our country, before we are powerful enough to have a good economy, and before we have taken from President Bush and the next administration billions and billions of more dollars -- no way that they can let you go," Karzai said, to nervous laughter from the audience.)

Among the challenges Obama's strategy faces: French President Fran?ois Hollande isn't budging from his campaign pledge to withdraw his country's roughly 3,600 combat troops by the end of 2012 ? one year sooner than his predecessor Nicolas Sarkozy had planned. Hollande suggested after talks with Obama at the White House on Friday that French forces could stay on to help train Afghan military and policy, but reiterated that an end to their combat role was "not negotiable."

Obama faces dual pressures at home: The war-weary American public wants out of Afghanistan, the country's longest war, but Republicans have blasted the president for setting a departure date, saying this will only embolden Islamist fighters and lead friendly Afghans to hedge their bets.

Mitt Romney, in an op-ed for the Chicago Tribune, accused Obama of failing to show leadership inside NATO and of putting America "on a path to a hollow military" and said he would reverse both trends. He did not detail his own Afghanistan policy.

The United States is on track to reduce its presence to 68,000 troops by late September. More than 3,000 Americans have been killed in the decade-long conflict launched to catch or kill Osama bin Laden, whom Navy SEALS shot dead in a dramatic May 2011 raid inside Pakistan.

That country closed supply lines for NATO forces after a November strike inside its territory killed 24 Pakistan soldiers. Negotiations to reopen them have yet to bear fruit. Pakistani President Asif Ali Zardari is attending the summit, but Obama has not plans to meet with him one-on-one.

"The president will certainly have a chance to see him and speak to him," Deputy National Security Advisor Ben Rhodes told reporters aboard Air Force One late Saturday.

"On the supply lines, we believe that this is going to be resolved," Rhodes said. "We expect that to take some time.?So there is still work to be done through those negotiations."

NATO leaders are also expected to take up the issue of Iran's suspect nuclear program, as well as how the alliance should respond to the bloody crackdown in Syria.

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