BRUSSELS — U.S. Vice President Mike Pence moved Monday to assuage European Union fears about the strength of Washington’s support for the union and its commitment to European security through the NATO military alliance.

In meetings in Brussels, Pence said he was acting on behalf of President Donald Trump “to express the strong commitment of the United States to continued cooperation and partnership with the European Union.”

“Whatever our differences, our two continents share the same heritage, the same values and above all the same purpose: to promote peace and prosperity through freedom, democracy and the rule of law,” he told reporters after talks with EU Council President Donald Tusk.

Trump’s election campaign rhetoric — branding NATO obsolete and vowing to undo a series of multinational trade deals — and his benevolence toward Russian President Vladimir Putin sparked anxiety in Europe. Trump was also supportive of Britain’s vote last year to leave the 28-nation EU, a withdrawal known as Brexit. And he has suggested that the EU itself could soon fall apart.

Tusk, who chairs meetings of the 28 EU states, said he had been reassured after “open and frank talks” with Pence but made clear that the EU bloc would watch closely to ensure the U.S. puts its words into action.

“I heard words which are promising for the future, words which explain a lot about the new approach in Washington,” Tusk said.

He underlined that “too many new and sometimes surprising opinions have been voiced over this time about our relations — and our common security — for us to pretend that everything is as it used to be.”

“We are counting as always in the past on the United States’ wholehearted and unequivocal   — let me repeat, unequivocal — support for the idea of a united Europe,” Tusk said. “The world would be a decidedly worse place if Europe were not united.” He asserted: “The idea of NATO is not obsolete, just like the values which lie at its foundation are not obsolete.”

Tusk added, “Both Europeans and Americans must simply practice what they preach.”

Pence voiced the administration’s strong support for NATO over the weekend and was due to visit the alliance’s headquarters later Monday.

Pence’s meetings were aimed at assuring European leaders that his words reflected the views of Trump and would not easily be swept away at the whim of the U.S. president or undermined by statements issued on Twitter.

Pence, as he did in an address Saturday at the Munich Security Conference, reaffirmed U.S. support for the NATO alliance and said Trump would demand that Russia honor its commitments to end the fighting in Ukraine. “In the interest of peace and in the interest of innocent human lives, we hope and pray that this ceasefire takes hold,” he said.