WASHINGTON — European leaders, anxious over Donald Trump’s unpredictability and kind words for the Kremlin, are scrambling to get face time with the new American president before he can meet with Russian President Vladimir Putin, whose provocations have set the continent on edge.

One leader has raised with Trump the prospect of a U.S.-European Union summit early this year, and the head of NATO — the powerful military alliance Trump has deemed “obsolete” — is angling for an in-person meeting ahead of Putin as well. British Prime Minister Theresa May is working to arrange a meeting in Washington soon after Friday’s inauguration.

For European leaders, a meeting with a new American president is always a sought-after — and usually easy-to-obtain — invitation. But Trump has repeatedly defied precedent, making them deeply uncertain about their standing once he takes office. Throughout his campaign and in recent interviews, Trump has challenged the viability of the EU and NATO, while praising Putin and staking out positions more in line with Moscow than Brussels.

“There are efforts on the side of the Europeans to arrange a meeting with Trump as quickly as possible,” said Norbert Roettgen, the head of the German Parliament’s foreign committee and a member of Chancellor Angela Merkel’s party.

Donald Tusk, the former Polish prime minister who heads the EU’s Council of member state governments, invited Trump to meet with the EU early in his administration, according to a European Union official.

Trump backs Britain’s exit from the European Union, casting the populist, anti-establishment movement as a precursor to his own victory. In a recent joint interview with two European newspapers, Trump said of the EU, “I don’t think it matters much for the United States.” And Trump’s praise for Putin and promise of closer ties to Moscow have deepened the uncertainty.

Trump’s top national security adviser has been in close contact with the Russian ambassador to the U.S., conversations that have involved setting up a phone call between the Putin and the president-elect, transition officials have said.

But Trump currently has no plans to meet with Putin, according to the senior adviser, who insisted on anonymity in order to discuss the transition team’s internal planning. Aides vehemently denied a recent report in The Sunday Times of London that Trump’s first foreign trip would be a summit with Putin in Reykjavik, Iceland, the site of a Cold War meeting between President Ronald Reagan and Soviet leader Mikhail Gorbachev.

Still, Europe’s leaders are eager to ensure they have Trump’s ear before Putin does. NATO Secretary General Jens Stoltenberg is hoping to meet with Trump quickly, perhaps in Washington, according to a NATO official. And even if Trump rejects a U.S.-EU summit, European officials are said to have discussed the prospect of a smaller meeting with the U.S. president and the heads of the continent’s most powerful countries, including Merkel.

A Putin meeting wouldn’t be without precedent. When Bill Clinton made his maiden trip to Vancouver in 1993, it was primarily for a summit with Russian President Boris Yeltsin.

Aides have signaled that one of Trump’s first foreign leader meetings at the White House will be with May, who became prime minister following Britain’s vote to leave the EU.

The president-elect’s team is also working on early invitations to Washington for the leaders of Mexico and Canada, according to the Trump adviser.