SEOUL — President Obama’s hopes of emerging from his Asia trip with the twin victories of a free trade agreement with South Korea and a unified approach to spurring global economic growth ran into resistance on all fronts yesterday, putting Obama at odds with his key allies and largest trading partners.

The most concrete trophy expected to emerge from the trip eluded his grasp: a long-delayed free trade agreement with South Korea, first negotiated by the Bush administration and then reopened by Obama, to have greater protections for US workers.

And as officials frenetically tried to paper over differences among the Group of 20 members with a vaguely worded communiqué to be issued today, there was no way to avoid discussion of the fundamental differences of economic strategy. After five largely harmonious meetings in the past two years to deal with the most severe downturn since the Depression, major disputes broke out between Washington and China, Britain, Germany, and Brazil.

Each rejected core elements of Obama’s strategy of stimulating growth before focusing on deficit reduction. Several major nations continued to accuse the Federal Reserve of deliberately devaluing the dollar last week in an effort to put the costs of America’s competitive troubles on trading partners, rather than taking politically tough measures to rein in spending at home.

The result was that Obama repeatedly found himself on the defensive. He and the South Korean president, Lee Myung Bak, had vowed to complete the trade pact by the time they met here; while Obama insisted that it would be resolved “in a matter of weeks,’’ without the pressure of a summit meeting it was unclear how the hurdles on nontariff barriers to US cars and beef would be resolved.

Obama’s meeting with China’s president, Hu Jintao, appeared to do little to break down Chinese resistance to accepting even nonbinding numerical targets for limiting China’s trade surplus. While Lael Brainard, the undersecretary of the Treasury for international affairs, said that the United States and China “have gotten to a good place’’ on rebalancing their trade, Chinese officials later archly reminded the Americans that as the issuers of the dollar, the main global reserve currency, they should consider the interests of the “global economy’’ and their own “national circumstances.’’

The disputes were not limited to America’s foreign partners. Treasury Secretary Timothy F. Geithner got into a trans-Pacific argument with one of his former mentors, Alan Greenspan, the former chairman of the Federal Reserve, after Greenspan wrote that the United States was “pursuing a policy of currency weakening.’’ Geithner shot back on CNBC that while he had “enormous respect’’ for Greenspan, “that’s not an accurate description of either the Fed’s policies or our policies.’’

Much of the rest of the world seemed to share Greenspan’s assessment. Moreover, Obama seemed to be losing the broader debate over austerity. The president has insisted that at a moment of weak private demand, the best way to spur economic growth is to have the government prime the pump with cheap credit and government stimulus programs. He quickly found himself in an argument with Prime Minister David Cameron of Britain and Chancellor Angela Merkel of Germany.

“You do hear the argument made sometimes: If you have a deficit, put off the action to deal with it because taking money out of the economy will reduce your growth rate,’’ Cameron said at the meeting. “I simply don’t accept that.’’

Merkel, in a more traditional German view reflective of her country’s history of hyperinflation before World War II, was equally adamant.

“I am not one, and Germany is not one, who says growth and fiscal consolidation are contradictory,’’ she said during a lunchtime address in Seoul. “They can go together, and it is essential to return to a sustainable growth path.’’ She also suggested that it was the job of deficit countries — like the United States and Britain, although she diplomatically avoided citing them — to increase their competitiveness rather than put limits on countries that had figured out how to get the world to buy their goods.

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