(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 François 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.