NATO head Jens Stoltenberg on Tuesday said he was sure Donald Trump would live up to all US commitments to the alliance, just days after urging the president-elect not to go it alone.

"President-elect Donald Trump stated during the election campaign that he is a big fan of NATO," Stoltenberg said in Brussels as he arrived for talks with EU defence ministers.

"And I am certain that he will be a president... who will live up to all the commitments of the United States in the alliance, because a strong NATO is important for Europe but it's also important for the United States."

Trump's upset election badly rattled nerves in Europe after he appeared to call into question Washington's near 70-year security guarantee by saying he would only help NATO allies if they paid their way.

He also appeared to be much more friendly towards Russia, praising President Vladimir Putin as a strong leader in marked contrast to a weak Barack Obama in Washington.

Asked about a telephone call between Trump and Putin on Monday in which the Kremlin said they agreed to improve relations, Stoltenberg denied this was cause for concern.

"First of of all, I think it is a very normal thing that president-elect Donald Trump speaks to world leaders, including of course the leader of Russia," he said.

"The message from NATO has been that we want dialogue with Russia ... Especially when tensions are high, especially when we face many different challenges, it is important."

Stoltenberg's upbeat tone came despite his stark warning in Britain's Observer newspaper on Sunday, in which he wrote that "going it alone is not an option... this is no time to question the partnership between Europe and the United States."

But the NATO chief noted Tuesday that the two sides were on the same page, saying Trump's call for the allies to increase defence spending was exactly what they were already doing.

"I absolutely agree with him; that has been the message from US leaders for many years," Stoltenberg said.

"The good thing is that we now see that Europeans are actually investing more in defence... therefore contributing to better burden sharing," he said.

Washington accounts for nearly 70 percent of NATO defence spending and has long urged its European allies to do more, stepping up the pressure after Russia's intervention in Ukraine.

The Ukraine crisis shook NATO out of years of complacency and defence cuts, with leaders agreeing to its biggest military build-up since the end of the Cold War based on a commitment to devote two percent of national output to defence.

The European Union -- of whose 28 members 22 also belong to NATO -- is also boosting military cooperation and on Monday approved a defence roadmap to boost the bloc's capabilities.

On Monday, US President Barack Obama said he was sure Trump would stand by US security commitments and that he would tell Europe there would be "no weakening" of the relationship.