"I do not believe that any country today can be great in isolation," European Council chief Donald Tusk told reporters in Brussels, referring to Trump's campaign slogan of "Make America Great Again".
"Europe and the United States simply have no option but to cooperate as closely as possible."
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"We would take this opportunity to invite you to visit Europe for an EU-US summit at your earliest convenience. This conversation would allow for us to chart the course of our relations for the next four years," they said in a letter of congratulations to Trump.
But former Polish prime minister Tusk struck a more sober tone in a statement to journalists at the 28-nation European Union's headquarters as he recalled that "Italians, Irish, Poles, Germans, Spanish" had helped build America.
"While respecting the democratic choice of the American people, we are at the same time aware of the new challenges that these results bring. One of them is this moment of uncertainty over the future of our transatlantic relations," he said.
With the EU still reeling from the shock of Britain's recent vote to leave, Tusk added: "The events of the last months and days should be treated as a warning sign for all who believe in liberal democracy."
Following Trump's victory, EU foreign ministers will hold a special meeting in Brussels on Sunday at the invitation of the bloc's foreign policy supremo Federica Mogherini.
They will have an "informal dinner to exchange views on the way forward in EU-US relations following the US elections," a spokeswoman for Mogherini said.
Separately Martin Schulz, the head of the European Parliament, urged Trump to show "responsibility" after a divisive campaign, adding that he had "managed to become the standard-bearer of the angst and fears of millions of Americans.
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