Britain’s decision to withdraw some forces from Iraq even as President Bush sends more American troops demonstrates a growing isolation of America from its allies, which is affecting other priorities, including in Afghanistan and Iran.

Europeans are resisting American demands that they play a greater military role against the Taliban resurgence in Afghanistan in part because they see America as too preoccupied with Iraq to craft an effective strategy. The erosion of political support in Italy for the Afghanistan mission forced Prime Minister Prodi to offer his resignation Wednesday.

Iraq also has reduced Mr. Bush’s leverage as he seeks international support for pressuring Iran to give up its nuclear program — a demand that Iran again rejected Wednesday.

“One of the reasons a U.S. withdrawal is so essential from Iraq is that until we do that, even our best allies aren’t going to help us out,” said retired Army General William Odom, a former director of the National Security Agency.

In the face of American pressure, “the Europeans are saying, ‘Why are we going to go into Afghanistan and get mired in a quagmire?”‘ said a former State Department policy-planning official, Henri Barkey. “People perceive that we don’t have a long-term strategy in Afghanistan. So why do you want to put troops where they will be targeted by the Taliban?”

Bush administration officials dismissed the significance of Prime Minister Blair’s announcement that Britain would withdraw 1,600 of its 7,100 troops from Iraq by summer. In a parallel announcement, Denmark decided to remove most of its 460 soldiers by August.

Secretary of State Rice, Vice President Cheney, and White House Press Secretary Tony Snow all called Mr. Blair’s move a sign of progress in southern Iraq, where British forces are based, and Defense Department spokesman Bryan Whitman rejected the notion that America was becoming more isolated.

“There are still 23 coalition members that have troops in Iraq,” he said. “We have always said every country will have to determine what its participation in the global war on terrorism will be.”

Democratic congressional leaders called the British and Danish decisions another indication that Mr. Bush’s move to send an additional 21,500 American forces to Iraq was a mistake. The Senate Armed Services Committee chairman, Senator Levin of Michigan, said the allies’ withdrawal “accelerates the breakup of the coalition in Iraq.”

General Odom called the British decision a sign that Mr. Bush can’t count any longer on support even from staunch allies.

“The news in this is that Mr. Blair’s government has undoubtedly read the intelligence reports and reached the obvious conclusion that it’s better to cut your losses,” said General Odom, now a professor at Yale University in New Haven, Conn. “If the British leave, it’s very difficult to pretend that we have a coalition.”

Anthony Cordesman, an Iraq expert at Washington’s Center for Strategic and International Studies, said the British drawdown “weakens the image of the coalition and further isolates the U.S.” In an analysis of Mr. Blair’s decision, Mr. Cordesman wrote: “This is a war of perceptions, as well as military power, and the influence of British cuts will be negative.”

Mr. Cordesman wrote that the British pullout reflects the reality that southern Iraq is now under the political control of Shiite forces that have little interest in promoting the power of the central government or Iraqi national unity, and that British forces have been unable to prevent or alter this development.

The operational commander of America’s forces in Iraq, Army Lieutenant General Ray Odierno, said yesterday that there is a power struggle in southern Iraq between rival Shiite groups.

If that competition turns violent, and British forces still in the area are unable to suppress it, it may be necessary to send in American troops or soldiers from another nation with forces in Iraq, General Odierno said in a teleconference with American journalists.

Meanwhile, the growing estrangement of America from its partners is weighing on troop commitments in Afghanistan, where more than 47,000 troops from America and other members of the North Atlantic Treaty Organization are battling the Taliban. NATO members such as Germany, France, and Italy are resisting America’s demands to commit more forces and lift restrictions on their use.

Mr. Prodi resigned after the Italian Senate failed to approve continued participation in the NATO mission. Italy has 1,800 soldiers in Afghanistan.