Updated

France, Germany and other European countries President Bush alienated during his first four years in office promised Wednesday to work with the newly re-elected U.S. leader.

Some European leaders expressed hope Bush would reach out to them in his second term. But others gloomily forecast no major tack in White House policy and continued trans-Atlantic bickering.

Markets reacted with relief to the end of the long, contentious race and a likely Bush win. European shares hit six-month highs and U.S. stocks also shot up.

Later Wednesday morning, Bush's challenger, Sen. John Kerry, called Bush to conced defeat, officials told The Associated Press.

"We have lots to do on current crises: Iraq, the Middle East, Iran, the challenges of the African continent, to rebuild, to renovate the trans-Atlantic relationship," French Foreign Minister Michel Barnier (search) said on RTL radio. "This is a new step that starts at a very important moment for the world."

German officials said close cooperation between Europe and the United States is essential, not only on Iraq and terrorism but on AIDS and the environment as well.

Ties were strained by Chancellor Gerhard Schroeder's (search) vehement opposition to last year's U.S.-led war in Iraq, although the two governments have since moved to repair relations.

German Foreign Minister Joschka Fischer (search) pledged close cooperation with the winner.

"I have said that we will continue to cooperate positively," Fischer told reporters. "In international politics, we face difficult challenges that cannot be mastered without close cooperation between Europe — including our country — and the United States."

Karsten Voigt, the German Foreign Ministry's top official for relations with Washington, said he hopes Bush will seize the chance for "a new beginning" with Europe.

"I hope that a re-elected President Bush would use the chance offered by his re-election for a new beginning in European-American and German-American relations," Voigt told ARD television, adding the U.S. leader would do well to "approach the Europeans ... and say, let us sit down and talk about where we have common interests."

"That is necessary on the Middle East, it is necessary and possible in fighting terrorism and in the question of the proliferation of weapons of mass destruction, but it is also needed in the question of AIDS, climate protection and other issues."

Although Germany has offered help rebuilding Iraq and is training new Iraqi police and military, Voigt said "the German military will not be sent to Iraq."

Before Kerry conceded the election, Russian President Vladimir Putin (search) said a Bush victory would mean the American people had not given in to terrorist threats.

"If Bush wins, I would feel happy that the American people have not allowed themselves to be scared and made the decision they considered reasonable," Putin said at a Kremlin news conference after talks with Italian Prime Minister Silvio Berlusconi (search).

Putin said U.S.-Russian relations have improved under Bush.

Berlusconi said a Bush victory would help maintain close ties between the United States and Italy.

"Bush will keep up that policy that gives the United States the role of promoting freedom in the world," he said.

Japanese Prime Minister Junichiro Koizumi (search), another U.S. ally in Iraq, and Thai Prime Minister Thaksin Shinawatra both said their nations would have good relations with the United States no matter who wins.

Iraq's interim Prime Minister Ayad Allawi (search) said his country will remain a friend of the United States no matter the outcome of the election.

"The United States have freed us from a dictator, from a very long period of wars and agony," Allawi told the Italian newspaper La Repubblica in an interview published Wednesday.

"We will always be grateful to America for what it has done and what it continues to do."

Australia's conservative government was one of Bush's staunchest allies and among the first to join the U.S.-led military coalition.

"From our point of view, the Bush administration is a known quantity," Australian Foreign Minister Alexander Downer (search) told Australian Broadcasting Corp. radio. "We've had a very good relationship with them for the last four years and I'm sure we'll be able to keep building on that over the next four."

In Indonesia, however, Muslim leader Syafii Maarif (search) said a Bush win was "a catastrophe."

"Bush has made a mess of the world over the last four years," he said.

Swedish Prime Minister Goeran Persson (search) predicted Bush will not revamp his policies and that the sniping between Europe and the United States would continue.

"Sweden and Europe will continue to criticize Bush the same way as earlier. But I do not believe that he will be more willing to listen to it."