WASHINGTON (AP) – Humbled by elections at home, President Bush is heading into talks with leaders in Asia and Europe who will be watching for signs of weakness, uncertainty or retrenchment.

Bush’s challenge is to demonstrate that U.S. leadership as the world’s last superpower is undiminished on the world stage.

“I think he will go vigorous, I think he’ll give a powerful performance,” said Kurt Campbell, a top Pentagon official in the Clinton administration who now is with the Center for Strategic and International Studies.

Some world leaders, particularly those who resented Bush’s cowboy swagger and saw his decision to invade Iraq in 2003 as a dangerous act of unilateralism, might be gloating privately at the president’s political misfortunes.

But the United States does not have a parliamentary system, and Bush will remain president for two more years. And other world leaders have been challenged at home, too, especially Iraq ally Tony Blair of Britain and war opponent Jacques Chirac of France, both of whom could commiserate with Bush.

The Democratic capture last week of both the House and the Senate on a tide of voter anger over Iraq diminished the president’s authority at home.

That’s resulted in “an interesting period here in Washington,” Bush told visiting Israeli Prime Minister Ehud Olmert this week. “You might realize the opposition party won, won the Senate and the House. And, what’s interesting, is that they’re beginning to understand that with victory comes responsibilities.”

On the world stage, Bush’s misfortunes could marginally embolden Chinese President Hu Jintao and Russian President Vladimir Putin. But, otherwise, it seems unlikely that geopolitical dynamics will be much changed.

“He acknowledges that he took a thumping. But leaders around the world take thumpings all the time,” said presidential historian Thomas E. Cronin of Colorado College. The election results also telegraphs to the rest of the world, “including Iraq and Russia, that we can have peaceful elections that alter the makeup of our national government,” Cronin said.

Bush was leaving Tuesday night for an eight-day tour of Asia, including stops in Singapore, Indonesia and Vietnam, where he attends a summit of Asian-Pacific nation leaders. At month’s end, Bush will travel to the Baltic Sea countries of Latvia and Estonia, once claimed by the Soviet Union, for a NATO summit in Riga, Latvia.

It will be Bush’s first trip to Vietnam. During the Vietnam War, he served in the U.S. in the Texas Air National Guard. Now, with the Iraq war dragging on for 3½ years and the U.S. death toll still rising, many of Bush’s critics are comparing Iraq to the Vietnamese quagmire.

Bush’s plan to arrive in Hanoi with a new pact normalizing trade with Vietnam hit an unexpected obstacle when the lame-duck GOP-controlled House failed to approve the measure on Monday. Its Republican sponsors had hoped to use another strategy to move the bill forward this week, but they put off the effort on Tuesday. It was an embarrassing setback as the president set out on his first postelection overseas trip.

He told a group of U.S. auto executives in the Oval Office on Tuesday that he would deliver this message to trading partners: “Just treat us the way we treat you. Our markets are open for your products, and we expect your markets to be open for ours, including our automobiles.”

Even before the elections, some of the go-it-alone tactics of Bush’s first term had already been replaced by great diplomacy, including U.S. efforts to rely on other countries to defuse nuclear tensions with North Korea and Iran.

“Some of the people who used to criticize us for unilateralism are now beginning to criticize us for not taking more decisive individual action,” said Stephen Hadley, the president’s national security adviser.

Not only is Bush under pressure at home from Democrats and some Republicans to change course on Iraq, but he is encountering calls from some U.S. allies, including most recently Blair, to reach out more to Iran and Syria in hopes of promoting broader stability in the region given the changing nature of the battle in Iraq.

Bush said Monday that Iran must first verifiably halt its enrichment of uranium as a precondition to talks. If Syria wants to contribute to the peace process, it should leave Lebanon for good and stop harboring terrorists, Bush suggested.

As presidential terms wind down, incumbents find themselves increasingly challenged in getting domestic programs through Congress and seem to prefer spending much of their time on foreign policy.

Nixon did it, traveling to Moscow to sign an arms-control agreement as the Watergate scandal was bringing down his government. Clinton did it after surviving an impeachment battle with the GOP-led Congress, spending the last days of his term trying to arrange a peace deal in the Middle East.

And Eisenhower did it after the Democrats swept the 1958 midterm elections, finding the only leverage he had at home was to veto bills, and preferring touring the world instead.

There’s a difference. Eisenhower was greeted as a hero. Clinton as he traveled drew huge crowds and affection. But Bush is widely disliked throughout much of the world.

Bush still has two more years in power, despite the midterm elections repudiating Republicans.

“The negative, obviously, is that he’s been repudiated,” said Fred Greenstein, a political science professor at Princeton University. “The positive is that he’s been chastised and tempered and we’re seeing much less of the my-way-or-the-highway approach to diplomacy and international relations.”