The Obama administration has made an urgent appeal for international donors to pledge more money to pay for Afghanistan’s security forces after the departure of U.S. and coalition combat troops at the end of 2014.

In formal diplomatic demarches sent to 64 countries this month, and in direct appeals by President Obama and top national security aides, the administration has outlined a $4.1 billion annual budget for the Afghan army and police, according to U.S. and foreign officials.

At least $1.3 billion would come from existing foreign donors, triple the amount they currently spend. The Afghan government would contribute $500 million, and the United States would pay the rest.

The request for indefinite commitments comes as the United States and its partners in Afghanistan are under pressure to cut costs and end an increasingly unpopular war.

The administration hopes to secure the pledges before a NATO summit in Chicago in May. So far, however, there have been no specific replies to the funding appeals, an administration official said.

“We’ve gotten a lot of questions and a lot of ‘We’re thinking about it,’ ” the official said.

U.S. officials and diplomats from Asian, European and Arab countries that received the appeal discussed the matter only on the condition of anonymity.

A diplomat from a close U.S. ally said his country shares the “objective” of maintaining a strong Afghan security force. “But,” the diplomat said, “we have a very restricted budget and a very severe fiscal situation.”

An Arab diplomat said his government wants more information on how the Obama administration arrived at its calculations, how much others will contribute and how the money will be administered within corruption-plagued Afghanistan. But, he said, “we’ll probably end up paying.”

Still others, particularly in Europe, pointed out that although U.S. money may flow more freely from the Pentagon than from the State Department, the opposite is true in their countries. Some said they will find it easier to pledge development funding for Afghanistan — a separate appeal for post-2014 money that will be made in July at an international conference in Tokyo — than to provide more military spending.

In December, Afghan President Hamid Karzai told the international community that after 2014, his country will need at least $10 billion annually in combined security and development assistance until 2025. Afghanistan’s gross domestic product is about $17 billion.

The United States spent about $12 billion last year, 95 percent of the total cost, to train and equip Afghanistan’s army and police. Since 2009, police salaries have been paid from a $5 billion development assistance fund established by Japan that will expire at the end of 2014.

The combined Afghan force is expected to reach a target strength of 352,000 in October. U.S. military officials have estimated that the force’s expenditure could be cut in half after this year once the target number is reached. The post-2014 budget also anticipates additional savings from a reduction in the size of the force of up to one-third by 2017, a projection that assumes successful reconciliation with the Taliban.

“I think as people consider the past and how to protect the past into the future, they’ll make the contribution, and we will have both a sufficient and sustainable” Afghan force, Marc Grossman, the administration’s special representative for Afghanistan and Pakistan, said last week during a fundraising tour in Europe.

The endgame envisioned for the war calls for a gradual transition of security control from foreign to Afghan troops throughout the country by some point next year, with all coalition combat forces to withdraw by Dec. 31, 2014. The administration’s main argument is that pledging more money now would ensure a smooth withdrawal and less future spending.

In formal notes sent to foreign capitals on March 10, the United States suggested pledges from individual countries in yearly amounts ranging from $500,000 to $250 million.

“I would say that the chances of setbacks goes up” with insufficient funding, Grossman said, “and goes down” with a robust and fully funded Afghan force.

The Afghan police, and to a lesser degree the army, have been much maligned in recent years as inept and corrupt. But as the Obama administration seeks more support for the force that is its ticket to exit the war, it has begun a steady drumbeat of praise for the Afghans’ improvements and achievements.

That effort has been undercut in recent weeks by a spate of attacks in which 16 NATO service members, including nine Americans, have been killed by Afghan troops or police officers. It is unclear whether the most recent attacks were in response to the shooting deaths of 17 Afghan civilians this month, apparently at the hands of a U.S. soldier.

In a Pentagon briefing Monday, Gen. John Allen, commander of the U.S.-led coalition, played down the incidents as “a characteristic of counterinsurgencies that we’ve experienced before,” in Vietnam and Iraq, and blamed them on enemy efforts “to disrupt both the counterinsurgency operations, but also disrupt the integrity of the indigenous forces.”

Although he acknowledged in congressional testimony his preference for a slow U.S. departure over the next two years and described tough fighting ahead, Allen expressed confidence that the Afghan force would be capable of taking over.

In an account he repeated at hearings in the Senate and the House, he spoke of a recent visit with Marines serving with Afghan forces in the southwestern province of Helmand as evidence of the close relationship between U.S. and Afghan troops.

With violence against Americans increasing across the country, he said, a young Marine told him that Afghan troops had offered to patrol “outside the wire for a couple of days” to protect their U.S. comrades.

“This one statement, spoken by a young Marine,” Allen said, “conveys the power of this brotherhood in arms forged in battle over the years. It speaks to the trust that we have built with the Afghans. . . . We know there is much hard and deadly work yet to be done, but the progress is real, and, importantly, it’s sustainable.”