YOKOHAMA, Japan — President Barack Obama claimed a stronger hand on the world stage Friday despite electoral defeats at home, failure to get a free-trade agreement with South Korea and lackluster international support for his get-tough policy with China on trade and currency disputes.

"It wasn’t any easier to talk about currency when I was first elected and my poll numbers were at 65 percent," Obama argued at the close of the G-20 summit, after bluntly accusing Beijing of undervaluing its currency.

The president flew to Japan for the APEC summit without the coveted trade pact with Korea or a united front with other countries against China’s currency policy. He also endured a gusher of criticism from other countries about a decision by the U.S. central bank to pump $600 billion into the U.S. economy, something China, Germany and others believe could weaken the dollar and lead to inflation.

Even so, the president contended that his standing with world leaders is not diminished.

"When I came into office people might have been interested in more photo-ops," the president said, because of the "hoopla surrounding my election."

But he contended he has now developed genuine friendships with leaders, including Indian Prime Minister Manmohan Singh, German Chancellor Angela Merkel and South Korean President Lee Myung Bak — and even Chinese President Hu Jintao.

"That doesn’t mean there aren’t going to be differences," the president added.

Those have been on stark display throughout the G-20 summit, which resulted in a final document in which leaders agreed on various measures to achieve economic stability, none of them enforceable or specific.

Obama contended this constituted victory nonetheless, even as he acknowledged that America’s place in the world has changed — and even if he wouldn’t say his had.

Whereas the U.S. had been the dominant superpower, "We are now seeing a situation where a whole host of other countries are doing well and coming into their own and naturally they’re going to be more assertive … and that’s a healthy thing," the president said.

Obama said progress was made in stabilizing and strengthening the global economy and it is now back on "the path of recovery." But he also warned nations "risk slipping back" into peril if they don’t work harder to foster sustained growth, end unfair trade practices and currency manipulation. Obama argued "countries with large surpluses must shift away from unhealthy dependency on exports," and said exchange rates "must reflect economic realities."

China’s currency "is undervalued," the president declared, adding that Beijing "spends enormous amounts of money" to keep the yuan in that condition. He said it’s critical for China, "in a gradual fashion," to let markets set the currency’s value.

But Obama’s summit partners declined to endorse his position, issuing a watered-down statement saying only they agreed to refrain from "competitive devaluation" of currencies. Using a slightly different wording favored by the U.S. — "competitive undervaluation" — would have shown the G-20 taking a stronger stance on China’s currency policy.

Of criticism from Germany and other quarters that the Federal Reserve Board engaged in what amounts to currency manipulation by purchasing $600 billion in U.S. Treasury bonds, the president said the move "was not designed to have an impact on the currency, the dollar. It was designed to grow the economy."

Critics have said the Fed’s action represented the very kind of "currency manipulation" that Washington has criticized in connection with China, because it could have the effect of devaluing the dollar and making U.S. exports cheaper.

On the global economy, Obama said while improvements have been made in a number of areas, he and other leaders recognize "progress hasn’t come quickly enough," particularly in the area of job creation.

"We have a recovery," he said when asked about lingering high joblessness in America.

"It needs to be speeded up. Government cannot hire back the 8 million people that lost jobs," he said. "That needs to be done by the private sector," he said of the economic woes back home in the United States.

Obama reiterated his intent to finalize a long-sought trade agreement with South Korea. A major sticking point remains access to the South Korean market for U.S. autos, but the president expressed confidence that the deal will get done.

"I think that we can find a sweet spot that works both for Korea and the United States," he said, adding he was not interested in a trade agreement for the sake of having one.

It was an embarrassing setback for a president who stressed the top objective of this trip was to cement agreements that would help create jobs at home, particularly through new trade opportunities with fast-growing economies such as China, India and Indonesia.

Obama will confront the same vexing trade and currency issues in Yokohama at the summit of the Asia-Pacific Economic Cooperation, which is expected to move on creation of a Pacific-wide free trade zone that would encompass more than half the world’s economic output.

Meantime, he sought to deflect talk of missed opportunities.

"The work that we do here is not going to seem dramatic. It is not always going to be world-changing. But step to step, what we’re doing is building stronger international mechanisms and institutions" that will help stabilize the world economy "and reduce tensions" among nations," Obama said.

"The easiest thing for us to do would be to take a passive role and just let things drift," the president said.