Big week for Obama on world stage. How did he do?

President Obama has wowed the world with his words and vision for addressing the major global challenges, from climate change and Middle East peace to the spread of nuclear weapons.

But the biggest foreign-policy week of Mr. Obama's young presidency – stretching from the United Nations in New York to the just-ended Group of 20 summit in Pittsburgh – demonstrates the difficulty of moving from appealing vision to leadership, especially in the 21st century of diffused global power.

The president will be able to claim some advances. These include a toughened international stance toward Iran in the run-up to talks that world powers will hold with Tehran next week. Also, any lingering doubts about Obama's stature and abilities have been erased, some foreign-policy analysts say, after he hosted a global economic summit and took the helm of the UN Security Council to win approval of new nuclear-nonproliferation measures. This was the first time an American president has chaired a Council session.

"It was perhaps Obama's best week in terms of foreign policy. I think he's proven to a range of leaders and the international public that at least in some cases, he's able to turn rhetoric into reality," says Charles Kupchan, a foreign-policy expert at the Council on Foreign Relations in Washington. "He went into the week with many different balls in the air and came out with concrete advances on a number of important issues."

Among the accomplishments Mr. Kupchan lists: tightening international constraints on the proliferation of nuclear weapons, forging a more united front in confronting Iran, bringing some consensus on reducing risk in the financial sector, and reaching agreement that the G20 will permanently replace the "old boys club" that he says the G8 had become.

Still, Obama did not get everything he wanted. Most glaring was a failure, after weeks of intense effort by his top diplomats, to be able to announce a restart of Israeli-Palestinian peace talks.

In the view of some international policy experts, what the president confronted this week is the 21st-century conundrum of a world that at once craves the leadership to address rising transnational threats, even as conflicting interests in an increasingly multipolar world feed resistance to American leadership.

"Obama hit what is perhaps the principal frustration of multilateralism in this era of rising middle economies and powers," says Steven Schrage, an international economics expert at the Center for Strategic and International Studies in Washington. "Much of the world chafes at seeing the US out front, but at the same time, no one else is able to fill that leadership role."

That resistance to American leadership was perhaps most vividly captured in the vitriolic UN speeches of leaders like Iran's Mahmoud Ahmadinejad, Libya's Muammar Qaddafi, and Venezuela's Hugo Chávez.

Mr. Chávez garnered repeated applause from the UN General Assembly with a speech on the theme of what he called "the two Obamas" – one who speaks of global cooperation and the other who leads like a traditional imperialist.

"Which is the real Obama, the powerless in this world want to know," he said.

Obama realizes that today's world is not one where any single leader can command global action, says Andrew Bacevich, a professor of international relations at Boston University. "After 9/11, President Bush acted as if all he had to do was clap his hands and the world would follow his lead," he says. "Obama doesn't kid himself on that score."

If anything, Obama took some steps this week to demonstrate he understands that international leadership today means working with many different countries and levels of power, some analysts say. In particular in his speech to the UN General Assembly, Obama hit some good notes, says Kupchan of the Council on Foreign Relations. "He made it clear the US is a team player again, the country that wants to make the UN a more central institution for decisionmaking."

While Obama's setback on Middle East peace was the major public failure of the week, some analysts say the near-absence of Afghanistan from the agenda means the week really proceeded without taking up the major foreign-policy issue before his administration. "Afghanistan is likely to be the crucial determinant of Obama's approach to foreign policy, and it was nowhere to be seen," Professor Bacevich says.

His point: "If Obama chooses to accept … [the] call for a full-fledged counterinsurgency campaign in Afghanistan, it will mean that in effect Obama is affirming the main thrust of US foreign policy since 9/11 – the idea of the 'long war,' " he says. "And that will mean that all these other interests – from reining in nuclear weapons to tackling climate change – will come to be seen as throwaway tasks."

Indeed, Obama closed the week and the G20 summit answering a question on Afghanistan. He said he's asking "some very tough questions" before deciding how to proceed.

Despite Obama's foreign-policy gains this week, Kupchan says, the president now faces crucial months that will tell if "the positive gains of the week are translated into real cooperation and progress on halting Iran's nuclear program, on climate change, and on the world economy."

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G20 summit wrap-up

The meeting yielded some success for both Obama and nations, but world leaders couldn't agree on an exit strategy for the economic stimulus. Click here to read more.

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