Obama on Afghanistan: Not a combat mission
Rasmussen also met with Zardari and said he was "encouraged" by their talk and believed Pakistan would re-open the supply lines in the "very near future."
As NATO leaders herald the Afghan war's end, they face the grim reality of two more years of fighting and more of their troops dying in combat.
Some NATO countries, most recently France, have sought to end their combat commitments early.
The Taliban and its allies have warned that they are waiting to fill the void in Afghanistan after NATO leaves.
Obama is eager to show election-year leadership on the world stage during the Chicago meetings.
Following a meeting with Karzai Sunday, Obama said NATO's drawdown plans mean that by 2014, "the Afghan war as we understand it is over." But he acknowledged enormous progress must be made for that to become a reality.
"We still have a lot of work to do, and there will be great challenges ahead," Obama said after his lengthy talks with Karzai. "The loss of life continues in Afghanistan."
Obama's words were echoed by other U.S. officials, who sternly warned that American forces and their allies should still expect to be engaged in battle even after Afghans take the lead.
"After this milestone in 2013 there still will be combat capability, combat authority and an expectation there will be combat," said retired Lt. Gen. Douglas Lute, the top White House national security council official in connection with the war.
Many alliance leaders, Obama chief among them, have a political incentive for trumpeting that drawdown plan, given the growing public frustration. Sixty six percent of Americans oppose the war, while only 27 percent support the effort, according to an AP-GfK poll released this month.
In France, voters elected President Francois Hollande in part because of a campaign pledge to pull his country's 3,300 troops out of Afghanistan ahead of schedule.
Since taking office, Hollande has said he plans to make good on his promise to bring combat troops home by the end of this year but will maintain French support for Afghanistan in other ways.
The U.S. and NATO will also maintain a sizeable and lengthy commitment to Afghanistan after combat troops come home at the end of 2014.
Sen. Jack Reed, D-R.I., a member of the Armed Services Committee who visits Afghanistan often, said that by 2014 Afghan forces, with the backing of international trainers and logistical support, "will be able to provide stability."
Speaking Monday on CBS' "This Morning," Reed said that Afghan leaders and the international community need to seek a political settlement "but the security forces will provide the foundation for the stability that is absolutely necessary as our troops withdraw."
Obama, in a trip to Afghanistan this month, signed a deal with Karzai detailing much of the U.S. commitment, including annual financing from Congress and support for development, health and education projects.
The U.S. may also leave a residual troop presence in Afghanistan, though any such step would require approval from the Afghans.
At the NATO conference, leaders were also discussing how the international community would finance Afghan security forces after 2014.
With none of the NATO countries having the stomach to pursue the war much longer, the only viable option is to support an Afghan army and police force capable of defending the country against the Taliban and its allies.
NATO estimates it will cost about $4.1 billion a year to finance the forces. The Afghan government will pay about $500 million of that, and the rest will come from donor countries, many of which are struggling with deficits and the specter of recession.
While the Chicago meeting was not billed as a pledging summit, leaders were discussing where the rest of the contributions would come from.
About $1.3 billion is expected to come from NATO members other than the United States. About $1 billion of that has already been pledged, a senior Western official said Sunday.
The official spoke on condition of anonymity because he wasn't authorized to disclose the figures. The U.S. and some nations outside the military coalition are expected to make up the $2.3 billion.
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