President-elect Donald Trump, left, spoke with Russian President Vladi­mir Putin on Tuesday and vowed to improve U.S.-Russia relations. (Evan Vucci/AP)

European and NATO defense officials cautioned President-elect Donald Trump on Tuesday about his warming relationship with Russian President Vladimir Putin, saying that they welcome dialogue but that the United States should not abandon its allies in a bid for improved ties with Moscow.

The warnings came hours after Trump and Putin spoke by telephone and vowed to work toward better relations, which have sunk to Cold War-era lows after Russia’s 2014 annexation of Crimea from Ukraine. 

Trump frequently praised Putin on the campaign trail, saying he is a stronger leader than President Obama. The Republican said during the campaign that if he were elected, he would reboot relations with the Kremlin to facilitate cooperation on a host of global challenges and “would look at” recognizing Crimea as part of Russia, a step that would legitimize a military takeover that most of the world says was illegal. The Kremlin said both teams were working on setting up a face-to-face meeting.

Although Putin did not officially back a candidate in the election, Kremlin-controlled media effusively praised Trump and belittled Democrat Hillary Clinton, who Putin believes backed demonstrators who protested his rule in 2011 and 2012.

The Monday conversation between Trump and Putin did not touch on some of the thorniest issues facing Russia and the West, such as Crimea and the conflict in eastern Ukraine, a Kremlin spokesman said Tuesday. A day earlier, Moscow said the two had discussed a “settlement for the crisis in Syria” and the prospect of joint efforts in the fight against global terrorism, notably the Islamic State.

Some European officials privately raised their eyebrows at Tuesday’s clarification from the Kremlin, saying they feared that it meant Trump was giving a green light to the annexation of Crimea.

European nations, led by Germany, have pushed hard against Trump’s rhetoric on Russia, and German Defense Minister Ursula von der Leyen said Tuesday that the president-elect should be cautious in his dealings with Putin.

“It is always good for us to remain in dialogue with Russia,” von der Leyen told reporters ahead of a meeting of European Union defense ministers in Brussels. “But for us it’s also important that we not forget our principles. That means that international laws should not be broken.”

Trump’s election has sparked fears among European nations that they will need to be more self-reliant on security matters, not only because the future U.S. leader pushed the issue on the campaign trail but also because some nations are wary of depending on security guarantees from a leader they see as having dangerously authoritarian tendencies. E.U. defense and foreign ministers met this week to put the finishing touches on efforts to bolster European defense initiatives that would give them more capabilities separate from the United States. The efforts were underway before the U.S. election, but they took on new urgency after Trump’s surprise victory.

The North Atlantic Treaty Organization — of which the United States is the most dominant member — also has been shaken by the election, with front-line countries such as Poland and the Baltic states struggling to divine Trump’s policy intentions. During the campaign, Trump said he would not automatically adhere to U.S. security guarantees in Europe and would “look into” rolling back sanctions on Russia that were imposed after the Crimea annexation.

Many far-right parties in Europe are celebrating the presidential victory of Donald Trump. (Jason Aldag,Ishaan Tharoor/The Washington Post)

“It is a very normal thing that President-elect Trump speaks to world leaders, including, of course, the leader of Russia,” NATO Secretary General Jens Stoltenberg said Tuesday. He said he was “certain” that Trump would live up to U.S. commitments. 

But Stoltenberg warned against abandoning countries that have taken hits from Russia in recent years.

“We think it is important to respect the territorial integrity and the sovereignty of all nations, including Ukraine,” he said.

David Filipov in Moscow contributed to this report.