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 about 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 left 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.