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Allies and critics of the United States joined Wednesday in praising Barack Obama on his re-election and piling pressure on the US president to use his second term to resolve the world's lingering problems, from the ongoing economic crisis to unresolved conflicts in Damascus and Kabul.

In Berlin, German Chancellor Angela Merkel led a chorus of European praise for Obama, with the United States' traditional allies looking for yet more openness and better trade ties from Washington.

"I look forward to continuing this (cooperation), so that both our countries can continue to work side-by-side to master the most important foreign and economic challenges that we face as friends and allies."

Merkel cited the pair's past "close and friendly cooperation" regarding the ongoing financial crisis, peacekeeping in Afghanistan and efforts to control Iran's nuclear programme.

David Cameron of Britain stressed cooperation on efforts to revive the world economy and resolve diplomatic conundrums, such as the Syrian conflict.

"There are so many things that we need to do: we need to kick-start the world economy and I want to see an EU-US trade deal," Cameron said in a statement.

In Brussels, European Union President Herman Van Rompuy and European Commission President Jose Manuel Barroso said Obama should help address "global challenges, including in the fields of security and economy." They also prioritized efforts to "unlock the unparalleled potential of the trans-Atlantic market."

EU-US relations have been strained by a carbon emissions dispute, while Europe has also come under pressure from Washington to resolve its long-standing debt crisis.

French President Francois Hollande, a socialist, said US voters had chosen "an open America" that believes in solidarity and multilateralism.

"It's an important moment for the United States, but also for the world," Hollande said.

"Your re-election is a clear choice in favour of an open America that shows solidarity and is fully committed to the international stage and aware of our planet's challenges: peace, the economy and the environment," he said.

Russian Prime Minister Dmitry Medvedev praised Obama as an "understanding and reliable" partner, who, unlike Republican challenger Mitt Romney, "the head of the most powerful country is not someone who believes that Russia is their biggest enemy."

Swedish Prime Minister Fredrik Reinfeldt praised Obama's "inclusive campaign" but noted that Obama faced major challenges since Congress was politically divided, and it remained to be seen how the president would be able to carry out his economic policy.

Belgian Prime Minister Elio di Rupo, one of Europe's first openly gay leaders, said Americans had opted for "a more just and more tolerant America," while financially troubled Spain breathed a sigh of relief, with Foreign Minister Jose Manuel Garcia-Margallo noting that Republican challenger Mitt Romney had promoted "extreme austerity" and opposed bond-buying programmes.

Outside Europe, Chinese leaders hailed the "positive progress" registered in bilateral ties during Obama's previous term, although a commentary by the government's Xinhua news agency said Obama's administration should now "set a more constructive tone in crafting its China policy" over the next four years.

India's leaders said they were looking forward to boosting ties, while Israel expected the Obama administration to continue its policy of looking after its security.

The Muslim world saw Egyptian President Mohammed Morsi wishing for Egyptian-US ties to be "enhanced to serve the two countries' joint objectives of justice, freedom and peace," and the Palestinians campaigned once again for a two-state solution and Israeli withdrawals along the 1967 borders.

Afghan President Hamid Karzai, who has had to manage growing pressure from citizens outraged by civilian casualties inflicted by US-led coalition forces fighting the Taliban insurgency, hoped for a further expansion in bilateral ties on "the basis of mutual interests of the two countries."

The Taliban urged Obama to end the US presence in Afghanistan and to devote the country's energies towards building goodwill.

"Obama should prevent the US from acting like the world's police and focus instead on solving of the problems of the Americans."

Even Pakistan President Asif Ali Zardari - whose relations with Obama have been strained by Osama bin Laden's - reached out to the US president, while Syrian state television remarked that Obama's victory "will not have any impact on Syria or the Middle East in general, as the policies of all US presidents are usually made to serve the interest of Israel."

Obama's victory was also greeted by, among others, Malaysia, Australia, Poland, Saudi Arabia, Mali, Nigeria, South Africa and the Dalai Lama.