French President Francois Hollande vowed a "firm" response to a growing list of pronouncements by the maverick tycoon, including his encouragement for Brexit and suspension of all refugee arrivals.
"We must conduct firm dialogue with the new American administration which has shown it has its own approach to the problems we all face," the French leader said after a meeting of southern EU countries in Lisbon, flanked by fellow leaders.
Hollande spoke out a day after Trump -- who has made clear he thinks other EU countries will leave the bloc -- called Britain's decision to leave the European Union a "wonderful thing".
"When he talks about Brexit being a model for other countries, I think we must respond," he said, adding that Trump's "protectionist" measures could "destabilise economies not just in Europe but the economies of the main countries of the world".
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British Prime Minister Theresa May, whose country voted to leave the EU last June plunging the bloc into an unprecedented crisis, became the first world leader to meet Trump in Washington yesterday.
Keen to forge a post-Brexit trade deal with the United States and other countries, she refused to condemn Trump's refugee suspension today.
"The United States is responsible for the United States' policy on refugees" she said when repeatedly pressed on the issue at a press conference in Turkey.
Luxembourg Foreign Minister Jean Asselborn condemned the tougher visa measures slapped on seven Muslim states: Iran, Iraq, Libya, Somalia, Sudan, Syria and Yemen.
"The decision is .. Bad for Europe, because it's going to strengthen even further the mistrust and hatred towards the West in the heart of the Muslim world," he told the Sunday edition of German daily Tagesspiegel, excerpts of which were released a day in advance.
The first concrete cases emerged today of US-bound travellers being turned back due to the new visa arrangements.
The French and German foreign ministers meanwhile voiced "concern" about Trump at talks in Paris.
"Welcoming refugees who are fleeing war is part of our duty," France's Jean-Marc Ayrault said following a meeting with his new German counterpart, Sigmar Gabriel.