WASHINGTON â€"  Mapping the way out of an unpopular war, the United States and NATO are trying to build an Afghan army that can defend the country after 130,000 international troops pull out. The alliance's plans for arm's-length support for Afghanistan will be a central focus of the summit President Barack Obama is hosting Sunday and Monday in Chicago.

The problem with the exit strategy is that someone has to pay for that army in an era of austerity budgets and defense cutbacks.

The problem for the United States is how to avoid getting stuck with the check for $4.1 billion a year.

"This has to be a multilateral funding effort," said Pentagon spokesman George Little. "We think there should be contributions from other countries."

That's partly why so many non-NATO nations are getting invitations to the summit. About 60 countries and organizations are expected to be represented, including nations such as Japan that are far removed from the trans-Atlantic defense pact's home ground.

More than 20 nations have already agreed to help fund the Afghan army and more are expected to announce their commitments at the Chicago summit. U.S. and other NATO leaders claim that fundraising is on track, although the totals publicly announced so far are small.

A senior Obama administration official said the U.S. and its partners would seek to set targets at the summit for the size and scope of the Afghan security forces after 2014, when foreign forces pull out. The official, who spoke on the condition of anonymity in order to preview the upcoming summit, would not detail pledges expected in Chicago.

That force is now projected to be smaller -- and cheaper -- than NATO had planned only a year ago. The decision to trim the goal for an Afghan force from about 350,000 to roughly 230,000 was driven more by economic reality than a shift in thinking about Afghanistan's security needs after 2014, U.S. military officials and NATO diplomats said. The officials spoke on condition of anonymity to discuss internal planning. The larger force had been projected to cost $7 billion a year.

Obama is unlikely to say so, but outside estimates of the U.S. share of the bill for Afghan defense after 2014 range from a quarter to well more than half the total bill. The U.S. will also be on the hook for other support to Afghanistan, but the amount is unclear. The United States is the richest and best-equipped nation in the NATO alliance and long Afghanistan's largest patron.

Obama signed a pledge with Afghan President Hamid Karzai this month that would obligate the U.S. for a decade. Several other nations have signed similar long-term deals, and NATO is to sign one with Afghanistan at the Chicago meeting. The agreements cover a range of assistance to Afghanistan, but underwriting the military is the largest line item.

The summit in Obama's adopted hometown is not a pledging conference, but it will be a platform for Obama to invite other nations to step up.

Follow-up conferences are planned for Kabul and Tokyo later this year, where specific pledges are expected.

U.S. officials have had their tin cups out for months. Marc Grossman, the top State Department official for Afghanistan, recently hit up European nations, and others are lobbying Russia, Central Asian and Asian nations. U.S. officials are asking for pledges to sustain an Afghan force of roughly 230,000 during the first three years after the NATO-led international force departs.

The argument is fairly straightforward. Even $4 billion a year to prop up the Afghan military is cheaper than the cost of maintaining a foreign army in Afghanistan, and a lot easier for war-weary publics to swallow.

Some of the requests appear to be largely symbolic. For example, U.S. officials asked some of Afghanistan's neighbors for initial pledges of about $5 million annually, said Richard Weitz of the Hudson Institute in Washington.

"That's nothing, but it's something, too," Weitz said, since it serves the diplomatic goal of showing broad support for Afghan stability.

Afghanistan has said it will contribute $500 million toward its own army. The goal is $2.3 billion from the U.S. and nations outside the fighting coalition, and $1.3 billion from coalition nations other than the U.S.

"You'll see a strong commitment from allies and partners, and from the Afghan government" in Chicago, NATO spokeswoman Oana Lungescu said.

The White House said Obama discussed continued support for Afghan forces during pre-summit phone calls Tuesday with the leaders of Australia and Italy.

Britain had already pledged $110 million annually beginning in 2015, and on Wednesday Australia announced that it will contribute $100 million annually for three years.

Afghanistan will dominate the agenda for the Chicago meeting, although there is likely to be little discussion of the military campaign itself. Karzai is attending and this week NATO invited Pakistani President Asif Ali Zardari.

NATO is eager to bring forces home but is pledged to a calendar agreed the last time the leaders met, in 2010. Under that agreement, NATO forces will remain in Afghanistan into 2014 and depart that year.

In Chicago, Obama and other NATO leaders will sign up anew to that schedule, even though a majority of Europeans and Americans now tell pollsters the war is not worth fighting and should end as quickly as possible. In Afghanistan this month, Obama said the war must end "responsibly," which cannot mean suddenly.

U.S. and other NATO officials have said there will be no new announcement of troop withdrawals during the Chicago conference. Largely because of public opposition to the war, NATO nations quietly tweaked the 2014 plan earlier this year. The overall deadline holds, but U.S. and other allied forces will shift into largely noncombat roles next year.

The Chicago summit had once been viewed as a possible showcase for progress toward peace talks and a political settlement between Karzai's government and the Taliban. There is no real gain to show, however. The insurgents walked away from U.S.-led talks in March. U.S.-backed peace initiatives to open a Taliban political office and transfer Taliban prisoners from the military prison at Guantanamo Bay, Cuba, are in limbo. Insurgents have assassinated the leader and a top lieutenant of the Afghan peace council.