President Barack Obama's eight-day overseas trip yielded success on a top goal: signaling to the world a new U.S. approach that breaks with the go it alone style of President George W. Bush.

But Obama had more limited gains during his trip to Europe and the Middle East on concrete issues like prodding allies to do more to stimulate the global economy and help on Afghanistan.

Obama headed back to Washington on Tuesday after an unscheduled stop in Baghdad, where he pushed Iraq's feuding factions to compromise and urged Iraqis to take responsibility for their country so U.S. troops could leave.

In cities from London to Prague to Istanbul, Obama got a rapturous welcome to his promise to listen and consult more, as he took his first turn on the world stage as president.

It made a high contrast with Bush, who was criticized for ignoring the advice of allies in his 2003 decision to invade Iraq and for failing to join the Kyoto climate treaty, an agreement Obama says he would have embraced.

Obama and his wife, Michelle, drew adoring crowds at campaign-style events in Europe where fans waved posters of him and media compared the couple's youth and glamour to the late U.S. president John F. Kennedy and his wife Jacqueline.

In Turkey, he won plaudits for his declaration that the United States is not, and will never be, at war with Islam.

But at the summit of the Group of 20 economic powers in London, European countries balked at his suggestion that they spend more to try to fight the global recession.

EXPECTATIONS

Europeans were similarly reluctant to heed a call to shoulder more of the burden in Afghanistan. They offered help with training of Afghan forces and humanitarian efforts but showed no new willingness to provide combat troops.

On balance the trip has gone extremely well. The Obama administration deliberately lowered its expectations on the specific issues, said Charles Kupchan, a scholar at the Council on Foreign Relations.

Although Obama had made clear that a call for fiscal stimulus was part of his message to the G20, aides stressed on the eve of the meeting that they did not necessarily expect countries to spend more right away.

Ahead of the NATO gathering, the White House said Obama's chief aim was to explain the revamped policy he had unveiled to address the worsening violence in Afghanistan. They said the effort to seek more resources would be an ongoing process.

He was able to get some things that he wanted and then there were other things that allies and others pushed back on, said Gary Schmitt of the American Enterprise Institute think tank. Ironically, I think they got about as much as they could get from our NATO allies on Afghanistan.

I think people were kidding themselves if they thought there were going to be significant amounts of more capable troops heading to Afghanistan, Schmitt said.

WHY DIDN'T THE WATERS PART?

Top Obama adviser David Axelrod mocked the notion that Obama achieved little on substance, telling reporters at a news briefing Tuesday that they seemed to be asking: Why didn't the waters part, the sun shine, and all ills of the world disappear because President Obama came to Europe this week?

The 47-year-old Obama was criticized as lacking seasoning in foreign affairs during last year's election campaign.

But the U.S. president, known as no drama Obama for his even temperament, did impress some leaders at both the G20 and NATO summits with his ability to broker disputes.

When China and France became deadlocked over the issue of how to regulate offshore tax havens, aides said Obama lowered the temperature of the meeting, paving the way for a deal.

Financial markets cheered the show of unity from the world leaders and French President Nicolas Sarkozy went out of his way to thank Obama, saying he helped find a consensus.

Obama also intervened when Turkey objected to a push by several European countries to name the Danish Prime Minister as the next leader of NATO. Turkey ended up dropping its objections, allowing Danish Prime Minister Anders Fogh Rasmussen to be named as the new secretary-general.

On the sidelines of the G20, Obama emphasized what he describes as his pragmatic approach to foreign policy when he held sitdowns with Russian President Dmitry Medvedev and Chinese President Hu Jintao.

While Bush talked about getting a sense of Vladimir Putin's soul when he first met the Russian president in 2001, Obama was more business-like. But aides said the meetings with both the Chinese and Russian leaders had gone well.

Still, neither country gave Obama immediate support when he sought a strong response from the United Nations Security Council to North Korea's firing of a long-range missile.

(Additional reporting by Ross Colvin in Washington and Crispian Balmer in Paris; editing by Andrew Roche)