US Vice-President Mike Pence assured the European Union in Brussels on Monday that the Trump administration will develop their cooperation in trade and security and backs the EU as a partner in its own right.

A month after Donald Trump caused alarm by renewing his endorsement of Brexit and suggesting others may follow Britain out of the EU, Pence told reporters that he had come to "the home of the European Union" with a message from the president.

Speaking of a "strong commitment ... to continue cooperation and partnership with the European Union", Pence added: "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."

At a later meeting at NATO across town, he made clear that US support for the Transatlantic defence alliance had a price, though; Trump, he said, "expects real progress" from European governments by the end of the year in increasing their spending on military budgets closer to a NATO target of 2 percent of GDP.

Donald Tusk, who chairs the European Council of EU leaders, told reporters that Pence had given him affirmative answers to three questions on Trump's support for: the current system of international law, NATO and "the idea of a united Europe".

"Reports of the death of the West have been greatly exaggerated," Tusk said, in a nod to American writer Mark Twain.

EU officials said they were encouraged by what they called Pence's clear assurances, including on US backing for holding the European Union together after Brexit, though they will watch closely to see how far Trump's actions match his deputy's words.

"We got everything we were looking for," one official said.

Pence noted the building of common European institutions after World War II and said: "With this union and in cooperation with the United States, history will attest that when the United States and Europe are peaceful and prosperous, we do advance the peace and prosperity of all the world."

Echoing comments he made over the weekend in Germany, Pence also addressed worries in Europe over Trump's suggestion that the NATO defence pact was "obsolete"; Washington, he said, was committed to defending the sovereignty and territory of European states and holding Russia to account for its actions in Ukraine.

Pence also repeated Trump's belief that "common ground" could be established with Russia after years of confrontation.

Europeans are concerned that Trump may prefer bilateral ties with European powers rather than working with the Union. Pence spoke of cooperation, including against Islamist violence: "The safety and security of your union and our people depends on that increased collaboration on the global fight against terrorism."