LONDON (Reuters) - World leaders offered to work with Donald Trump when he takes over as U.S. president, but expressed anxiety over how he will handle problems from the Middle East to an assertive Russia and whether he will carry out a number of campaign threats.

Several authoritarian and right-wing leaders hailed the billionaire businessman and former TV show host, who won the leadership of the world’s most powerful country against the odds in Tuesday’s election.

China, a target of Trump’s ire during his campaign, appealed for cooperation. Mexico also struck a conciliatory tone, despite Trump’s insults to Mexican migrants and pledges to build a wall to separate the two countries. South Korea urged him not to change policy on North Korea’s nuclear tests.

Trump, who has no previous political or military experience, said after defeating Democrat Hillary Clinton that he would seek common ground, not conflict, with the United States’ allies.

In the election campaign, he voiced admiration for Russian President Vladimir Putin, questioned central tenets of the NATO military alliance and suggested Japan and South Korea should develop nuclear weapons to shoulder their own defense burden.

Putin was among the first to send Trump congratulations.

Ties between Washington and Moscow have become strained over the conflicts in Ukraine and Syria, and allegations of Russian cyber attacks featured in the election campaign.

“It is not an easy path, but we are ready to do our part and do everything to return Russian and American relations to a stable path of development,” said Putin, for whom an easing of U.S. economic sanctions would be a prize.

Among other issues causing concern among allies are Trump’s vows to undo a global agreement on climate change, ditch trade deals he says have been bad for U.S. workers, and renegotiate the nuclear accord between Tehran and world powers which has led to an easing of sanctions on Iran.

Iran urged Trump to stay committed to the Iran deal. President Hassan Rouhani said the nuclear accord with six world powers could not be dismissed by one government.

UNCERTAINTY

German Chancellor Angela Merkel -- denounced by Trump as “insane” for allowing more than 1 million migrants into the country last year -- added a stern note in her message of congratulations which hinted at a certain unease.

“Germany and America are bound together by values - democracy, freedom, respecting the rule of law, people’s dignity regardless of their origin, the color of their skin, religion, gender, sexual orientation or political views,” Merkel said.

“On the basis of these values, I am offering to work closely with the future President of the United States Donald Trump.”

In Britain, where Trump’s victory had echoes of June’s referendum in which voters showed dissatisfaction with the political establishment by voting to leave the European Union, Prime Minister Theresa May said the “enduring and special relationship” between the two countries would remain intact.

But Scotland’s first minister, Nicola Sturgeon, who has often expressed distaste for Trump, said many people in the United States and across the world would feel “a real sense of anxiety.”

Nigel Farage, a leader of the Brexit campaign who spoke at a Trump rally during the election campaign, tweeted: “I hand over the mantle to @RealDonaldTrump! Many congratulations. You have fought a brave campaign.”

Some European officials however took the unusual step of openly denouncing the outcome, calling it a worrying signal for liberal democracy and tolerance in the world.

“We’re realizing now that we have no idea what this American president will do,” Norbert Roettgen, the head of the German parliament’s foreign affairs committee, said.

President Francois Hollande said France wanted to begin talks with Trump immediately to clarify his stance on international affairs.

“This American election opens a period of uncertainty,” Hollande said.

Slideshow ( 21 images )

French officials had endorsed Clinton and warned that Trump’s “confused” foreign policy objectives were alarming for the rest of the world.

“The U.S. is a vital partner for France and what’s at stake is peace, the fight against terrorism, the situation in the Middle East, economic relations and the preservation of the planet,” Hollande said.

But like-minded right-wing European parties that are hoping to make inroads of their own in 2017 -- a year in which Germany, France and the Netherlands hold elections, and Italy and Britain could also do so -- hailed Trump’s victory.

France’s far-right National Front leader, Marine Le Pen, said she hoped the same kind of upset would happen in France.

“The Americans gave themselves a president of their choosing and not the one that the establishment wanted them to rubber-stamp,” she said.

Slideshow ( 21 images )

PARTNERS AND ALLIES

Mexican President Pena Nieto, who was criticized for receiving Trump in Mexico during the campaign, said he was ready to work with the president-elect.

“Mexico and the United States are friends, partners and allies and we should keep collaborating for the competitiveness and development of North America,” Pena Nieto said.

Trump has said he could tear up the North American Free Trade Agreement (NAFTA), saying that it has killed U.S. jobs, and he called Mexican immigrants rapists during his campaign.

Sounding conciliatory, Chinese President Xi Jinping said Beijing and Washington shared responsibility for promoting global development and prosperity.

“I place great importance on the China-U.S. relationship, and look forward to working with you to uphold the principles of non-conflict, non-confrontation, mutual respect and win-win cooperation,” Xi told Trump, who had pledged to take on China and to tax Chinese imports to stop currency devaluation.

South Korea expressed the hope that Trump would maintain current U.S. policy of pressuring North Korea over its nuclear and missile tests. Seoul was concerned Trump may make unpredictable proposals to North Korea, a ruling party official said, quoting top national security officials.

A Japanese government official, speaking before Trump clinched the election, urged him to send a message as soon as possible to reassure the world of the United States’ commitment to its allies.

“We are certainly concerned about the comments (Trump) has made to date about the alliance and the U.S. role in the Pacific, particularly Japan,” the Japanese official said.

In the Middle East, Israel’s Benjamin Netanyahu, who had a poor relationship with President Barack Obama, said he hoped to reach “new heights” in bilateral ties under Trump.

Obama and Netanyahu sparred over the issue of Israeli settlements, while Trump has said they should expand.

Palestinian President Mahmoud Abbas also congratulated Trump, but analysts said his rule may be profoundly negative for Palestinian aspirations.

And despite Trump’s negative rhetoric about Muslims during his campaign, including threats to ban them from the United States, Egyptian President Abdel Fattah al-Sisi said he hoped the business magnate’s election would breathe new life into U.S.-Egyptian ties.