Politicians worldwide took stock Wednesday of Donald Trump's shock US election victory, with the president-elect winning praise from far-right figures and cautious welcome from key US allies.

In a message of congratulations to Trump, Russian President Vladimir Putin "expressed hope for mutual work on bringing US-Russia relations out of their critical condition", pledging to "do our part."

Chinese foreign ministry spokesman Lu Kang: "We look forward and we hope to work with the new US government to ensure a steady and sound development of bilateral ties".

NATO Secretary General Jens Stoltenberg: "US leadership is as important as ever... A strong NATO is good for the United States, and good for Europe."

European Council President Donald Tusk and European Commission President Jean-Claude Juncker, the EU's top officials: "Today, it is more important than ever to strengthen transatlantic relations."

South Korean President Park Geun-Hye said Seoul and Washington's coordinated policy of pressuring North Korea must remain "unaffected under the new US administration".

British Prime Minister Theresa May said: "Britain and the United States have an enduring and special relationship based on the values of freedom, democracy and enterprise ... I look forward to working with President-elect Donald Trump, building on these ties to ensure the security and prosperity of our nations in the years ahead."

French President Francois Hollande said that Trump's win opened a "period of uncertainty."

Hungarian Prime Minister Viktor Orban, who leads a right-wing coalition with a strong anti-immigration stance: "Congratulations. What a great news. Democracy is still alive."

French politician Marine Le Pen, head of the far-right anti-immigration National Front (FN) party: "Congratulations to the new president of the United States Donald Trump and to the free American people".

German Foreign Minister Frank-Walter Steinmeier: "I think that we must expect that American foreign policy will become less predictable for us and we must expect that the United States will be more inclined to make decisions on its own. In other words, and I will not dress it up, nothing will become easier, many things will become more difficult".

Italian Prime Minister Matteo Renzi: "We are going through a great period of change, also on the international stage. I congratulate the new US president and wish him well in his job. Italy's friendship with America is solid."

Matteo Salvini, leader of Italy's far-right anti-immigration party the Northern League: "Now it's our turn."

Japanese Prime Minister Shinzo Abe, offering "heartfelt congratulations": "Japan and the United States are unshakeable allies connected by common values such as freedom, democracy, basic human rights and rule of law."

Iran's Foreign Minister Mohammad Javad Zarif: "Every US president has to understand the realities of today's world. The most important thing is that the future US president sticks to agreements, to engagements undertaken."

Polish President Andrzej Duda: "We are particularly pleased that during this year's NATO Summit in Warsaw the US decided to increase its military presence in Poland, thereby strengthening the Alliance's Eastern flank.

"We sincerely hope that your leadership will open new opportunities for our cooperation based on mutual commitment."

Turkish Prime Minister Binali Yildirim: "We hope our alliance with the United States will continue and that our partnership and relationships will develop."

Israeli Education Minister Naftali Bennett, head of the hardline Jewish Home party: "Trump's victory is an opportunity for Israel to immediately retract the notion of a Palestinian state in the centre of the country, which would hurt our security".

Palestinian president Mahmud Abbas: "We are ready to deal with the elected president on the basis of a two-state solution and to establish a Palestinian state on the 1967 borders."

Dutch Foreign Minister Bert Koenders: "We will judge him by his deeds."

Afghan President Ashraf Ghani "wishes success for Donald Trump on his new responsibility".

Malaysian Prime Minister Najib Razak: "Mr Trump's success shows that politicians should never take voters for granted."

Singapore's Prime Minister Lee Hsien Loong: "Like the Brexit referendum in June, Mr Trump's victory is part of a broader pattern in developed countries -- reflecting a deep frustration with the way things are, and a strong wish to reassert a sense of identity, and somehow to change the status quo."

Lech Walesa, Nobel peace prize winner and former Polish president: "We have to fix the democratic system because if we do not, we will see more of this kind of incident or, worse, democracy will find itself out on the street."