The sentiment around Europe's far-right is one of anticipation, as they hope for a continuation of the emboldened surge of right-wing populism facilitated by the first Trump election in 2016. Meanwhile, the rest of the political world warns of the perilous road Europe is facing.

Donning "Make Europe Great Again" caps, European far-right lawmakers celebrated Donald Trump's US election victory on Wednesday, expressing hope that the "historic moment" will boost their political cause.

In a social media video several members of the Patriots for Europe group congratulated Trump from the corridors of the European Parliament in Brussels, with the Village People's YMCA as soundtrack.

The unpredictable Republican's return to the White House showed "the will of the people for a bold new direction," the parliamentarians from Spain's Vox party, Austria's FPO, and Hungary's Fidesz said.

"Now it's time for us in Europe to follow suit," the video message said.

Fidesz is the party of Hungarian Prime Minister Viktor Orban, Trump's closest ally in Europe, who is playing host to a meeting of the bloc's 27 leaders in Budapest from Thursday.

Separately, Siegbert Droese of Germany's AfD, took the chance to publicly wish "all the best" on this "happy day" to the 78-year-old president-elect, as he asked a question during a grilling of would-be European commissioners by parliamentarians.

Trump's election was "a good example for our nations" Droese said, a red Make America Great Again cap sitting prominently on his desk.

The tone was very different on the centre and the left, after Trump sealed a dramatic comeback to power sweeping to victory against Democrat Kamala Harris.

"We must, more than ever, assert Europe as a power," said France's Pascal Canfin, of the centrist Renew. "Faced with Trumpism and its clones who want to destroy Europe from within, let's not give in".

Raphael Glucksmann of the Socialists and Democrats said the election put "every European leader before his responsibilities", calling for a stronger support of Ukraine and a boost of Europe's defences.

Manfred Weber, leader of the centre-right EPP, the largest group in the European parliament congratulated Trump, adding the vote marked "a historic turning point" for the EU.

"Europe must protect its interests sovereignly and independently without neglecting a strong transatlantic cooperation," he said.

"We must be able to take our own role in the world. The focus is now on building a European defence union and a strong European pillar of NATO."

Many in Brussels were jittery about the prospect of a Trump win ahead of the vote, fearing a reduced US commitment to European security and a curtailing of military support for Ukraine.

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