US president-elect Donald Trump's criticism of NATO has been met with "concern" by the military alliance's top offical, German Foreign Minister Frank-Walter Steinmeier said Monday.

Trump chided NATO in an interview published Sunday, accusing the alliance's 27 other member countries of not paying their fair share and of being ineffective on matters of global security.

"It's obsolete because it wasn't taking care of terror," Trump told Germany's Bild newspaper and the Times of London.

"With that being said, NATO is very important to me," Trump added.

Steinmeier said he held discussion with NATO Secretary General Jens Stoltenberg early Monday in which "the statements of president-elect Trump have, of course, been met with concern."

Spanish Foreign Minister Alfonso Dastis said it was possible Trump "changes opinion" in his criticism of NATO once he is sworn into office.

"I hope that as Donald Trump gets to know the European Union and NATO from the inside and participates in their work, he changes his opinion," he said at meeting of EU foreign ministers.

The Russian government, which has been in a protracted quarrel with NATO over the Western alliance's deployments in Poland and the Baltics, said Monday that it agreed with Trump's assessment.

"NATO is, indeed, a vestige," Kremlin spokesman Dmitry Peskov said, according to Russian state news agency TASS.

"We have long been speaking about our views on this organization," he said.

The US and European Union have imposed sanctions on Russia over its involvement in the ongoing conflict in eastern Ukraine.

Last month, President Barack Obama ordered additional sanctions, charging that the Russian government directed hackers to infiltrate US Democratic Party computers and leaked documents to influence the November 8 presidential election.

In the joint interview, Trump said Washington could potentially remove the sanctions in exchange for a reduction in nuclear arms.

"Let us be patient and wait till the moment Mr Trump takes office. Then we will be able to pass judgements on his initiatives," Peskov said.

Trump's frequent expressions of admiration for Russian President Vladimir Putin during his campaign and presidential transition have raised eyebrows in Washington.

A US Senate committee announced last week that they were launching an investigation into the ties between Trump's campaign and the Russian government, after questions were raised by the release of a dossier containing unverified claims that Moscow has compromising material on Trump.

At the meeting in Brussels, Trump did have one foreign minister come to his defence.

Hungarian Foreign Minister Peter Szijjarto told reporters that Trump's comments on NATO had been taken out of context

The president-elect said that the organization was obsolete "because it wasn't taking care of terror," he pointed out.

"Who would dispute the statement that NATO could have stepped up more powerfully and successfully in the fight against terrorism?" Szijjarto said.

A NATO spokesperson said Stoltenberg is "looking forward" to working with Trump, noting that discussions have already been held with the president-elect on countering terrorism and the need for increased defence spending in the alliance.