Europe is facing a “period of uncertainty” following the election of Donald Trump as US President, leaders have warned as France and Germany gave the President-elect a frosty welcome.

François Hollande, who once said the Republican candidate made him “want to retch”, called for European nations to unite to defend their interests.

The French President said Wednesday’s shock result “opens a period of uncertainty” that must be met with lucidity and clarity.

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“I offer my congratulations, as it is natural to do between two heads of democratic states,” Mr Hollande said in an unsmiling televised address. “The United States is a partner of the first order for France.

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“What is at stake is peace, the fight against terrorism, the situation in the Middle East, economic relations and the preservation of the planet.”

Hinting at climate change, previously denied by Mr Trump, Mr Hollande said he would open discussions with the new administration without delay but confront disagreements with “vigilance and frankness”.

“Some positions taken by Donald Trump during the US campaign contradict values and interests we share with the United States,” he added.

“This context calls for a united Europe, capable of making itself heard and of promoting policies wherever its interests or its values are challenged.”

Mr Trump has raised hackles in France by claiming Isis’ Paris attacks last November might have been avoided if the country relaxed its gun laws, as well as claiming “vicious” no-go zones existed in the capital.

In Germany, Chancellor Angela Merkel congratulated the President-elect and offered “close cooperation”, but tacitly criticised Mr Trump in her speech. She told reporters in Berlin his election campaign featured “confrontations that were difficult to bear”.

Ms Merkel stressed Germany's close historical connection with the US but added: “Germany and America are connected by values: democracy, freedom, respect for the law and for the dignity of human beings, independently of origin, skin colour, religion, gender, sexual orientation or political views.

“On the basis of these values, I am offering the future President of the United States of America, Donald Trump, close cooperation.”

Her remarks came after Mr Trump took aim at the German government’s policy of opening its borders to refugees, calling the move a “disaster in August”.

Francois Hollande and Angela Merkel made strong statements on the election of Donald Trump (Reuters)

“Hillary Clinton wants to be America's Angela Merkel and you know what a disaster this massive immigration has been to Germany and the people of Germany,” he told a rally, in comments since shown to be factually unfounded. “Crime has risen to levels that no one thought they would ever, ever see. It is a catastrophe.”

The response from Germany and France was far more outspoken than the cordial welcome offered by British leaders. Theresa May, the Prime Minister, congratulated Mr Trump and said she would maintain the “special relationship” between Britain and America, while Boris Johnson said he was “looking forward” to working with the new administration as Foreign Secretary.

Hungary’s Prime Minister was also positive, calling the shock result “great news” that shows “democracy is still alive”. Viktor Orban has previously been criticised by the US, including by Hillary Clinton when she was Secretary State, for weakening democracy and is known for his anti-refugee policies

Far-right and anti-immigration groups were also celebrating. Among them were France’s Front National, who hailed the “collapse” of political order and Dutch anti-Islam politician Geert Wilders.

Vladimir Putin said Moscow is ready to try to restore good relations with the US in the wake of the election but would face a "difficult path".

EU Parliament president Martin Schulz said the result “must be respected” as he said that Mr Trump “managed to become the standard-bearer of the angst and fears of millions of Americans”.