WASHINGTON — President Obama is facing challenges to American power on multiple fronts as he prepares for his first trip overseas since taking office, with the nation’s economic woes emboldening allies and adversaries alike.

Despite his immense popularity around the world, Mr. Obama will confront resentment over American-style capitalism and resistance to his economic prescriptions when he lands in London on Tuesday for the Group of 20 summit meeting of industrial and emerging market nations plus the European Union.

The president will not even try to overcome NATO’s unwillingness to provide more troops in Afghanistan when he goes on later in the week to meet with the military alliance.

He seems unlikely to return home with any more to show for his attempts to open a dialogue with Iran’s leaders, who have, so far, responded with tough words, albeit not tough enough to persuade Russia to support the United States in tougher sanctions against Tehran. And he will be tested in face-to-face meetings by the leaders of China and Russia, who have been pondering the degree to which the power of the United States to dominate global affairs may be ebbing.

Mr. Obama is unlikely to push for specific commitments from other countries on stimulus spending to bolster their own economies, White House officials acknowledged Saturday in a teleconference call, despite the fact that administration officials would like to see European countries, in particular, increase their spending to try to prompt a global economic recovery.

“Nobody is asking any country to come to London to commit to do more right now,” said Michael Froman, deputy national security adviser for international economic affairs. Instead, world leaders at the meeting will try to “do whatever is necessary to restore global growth,” Mr. Froman said.

The challenges stem in part from lingering unhappiness around the world at the way the Bush administration used American power. But they have been made more intense by the sense in many capitals that the United States is no longer in any position to dictate to other nations what types of economic policies to pursue — or to impose its will more generally as it intensifies the war in Afghanistan and extracts itself from Iraq.

“There is a direct challenge under way to the paradigms that America has been trying to sell to the rest of the world,” said Eswar S. Prasad, a former China division chief at the International Monetary Fund. The American banking collapse, which precipitated the global meltdown, has led to a fundamental rethinking of the American way as a model for the rest of the world. Yet even as his presence stirs opposition to particular American policies, Mr. Obama is being welcomed by many Europeans as an embodiment of American ideals.

In Prague, where Mr. Obama will stop later in the week, local officials are installing a hot line for residents to find out about street closings. In Strasbourg, France, site of a NATO meeting, protesters are planning an “international resistance camp” with antiwar actions designed to press Mr. Obama to get American troops out of Afghanistan. In Istanbul, his last stop, workers are polishing up the Hagia Sophia basilica-cum-mosque-cum-museum for the expected visit.

“The rest of the world is yearning for him,” said Kenneth Rogoff, a Harvard economist. “On the one hand, they’ll all be criticizing him, and criticizing the American model. But they all want to hear that he does have a miracle to deliver.”

The quandary has left senior advisers to Mr. Obama scrambling to come up with a way for him to project both American power and the new cooperative international model that his aides have been promising.

Mr. Obama will try to show confidence that his stimulus and economic program will work, administration officials said, while conceding that it may take time. He will say that he has put all the pieces in place to fix the American economy, while acknowledging that in a global system nations cannot put up walls to protect their individual economies.

Robert D. Hormats, vice chairman of Goldman Sachs International, said the president “must demonstrate to the world that he understands that it’s not just about saving ourselves.”

And Mr. Obama must try to do all of that in the middle of a global recession for which most of the world blames the United States. “The U.S. brand name has clearly suffered from this crisis, and the rest of the world is no longer willing to sit quietly and be lectured by the United States on how they should conduct economic policy,” Mr. Rogoff said.

A senior Obama administration official acknowledged that it would be harder for Mr. Obama to exhort other countries to adopt the American model. But Robert Gibbs, the White House spokesman, said Saturday in the conference call that Mr. Obama “is going to listen in London, as well as to lead.”

“Many of the things we’ve done in the past week demonstrate that America is leading by example,” he said.

In the past, American officials traveled to India, Brazil, China and South Africa and lectured government officials on the need for open markets, free trade and deregulation. But now some of those very policies — particularly deregulation — are viewed as the culprits for the recent economic collapse.

“Emerging markets now think they can do what they want without hectoring from the United States,” said Mr. Prasad, the former monetary fund official.

Compounding the problem for Mr. Obama is that the route that he has chosen to lead the United States out of the mess — heavy government spending — is not available to many other countries. European governments, for instance, are far more lukewarm about enormous stimulus programs because they already have strong social safety nets, and more fears of inflation, than does the United States.

So when Mr. Obama meets with other world leaders in London, he will be confronting a philosophical divide, with the United States on the defensive not just on economic issues like trade and financial regulation but also on a variety of national security and diplomatic matters.

After he leaves London, Mr. Obama will go to the French-German border for a NATO meeting at a time when European governments, under pressure from their populations, are looking for the exit doors in Afghanistan even as the United States sends more troops and money.

Administration officials had initially said they hoped to get more troop contributions at the NATO meeting; now they do not even talk about securing more troops from the Europeans, in a tacit acknowledgment that the forces will not be coming.

“I hope that Afghanistan will not be Obama’s war, because it should be owned by all of us,” said NATO’s secretary general, Jaap de Hoop Scheffer.

But there are already twice as many American troops as NATO troops in Afghanistan, and “Europe will never be able to match the numbers of the Americans in Afghanistan,” Mr. de Hoop Scheffer said. The NATO summit meeting, he said, “will not be about troop contributions.”

In Prague, Mr. Obama will confront an Eastern Europe nervous about Russian attempts to reassert itself in an area that Moscow views as its backyard. Mr. Obama has taken pains to reassure Russia that his administration will tread carefully regarding Bush administration plans to locate a missile defense system in Poland and the Czech Republic.