US President Donald Trump's defense secretary on Thursday said he did not see possible military collaboration with Russia for now.

The remarks signal that prospects for any significant cooperation between the US and Russian militaries against Islamic State in Syria is unlikely anytime soon.

They came despite repeated suggestions by Trump during his election campaign of the possibility of joint action against Islamic State militants.

"We are not in a position right now to collaborate on a military level. But our political leaders will engage and try to find common ground," Jim Mattis told reporters after talks at NATO headquarters in Brussels, also mentioning US concerns about Russian interference in democratic elections.

Just hours before Mattis spoke, Russian President Vladimir Putin said it was in the interests of both nations to restore communications between their intelligence agencies.

"It's absolutely clear that in the area of counterterrorism, all relevant governments and international groups should work together," he told Russia's Federal Security Service.

Monday's resignation of national security adviser Michael Flynn, who was seen in Moscow as a leading advocate of warmer ties with Russia, has underscored for the Kremlin the difficulties of reaching a settlement.

Flynn resigned after disclosures he had discussed US sanctions on Russia with the Russian ambassador

to the US before Trump took office, and that he later misled Vice-President Mike Pence about the conversations.

Asked whether he believed that Russia interfered in US presidential elections, Mattis said: "Right now, I would just say there's very little doubt that they have either interfered or they have attempted to interfere in a number of elections in the democracies." He did not explicitly cite the US election.

A Kremlin aide said there had been no progress on a potential meeting between Trump and Putin.

Mattis, who has previously accused Russia of trying to break the NATO alliance, told a closed-door session of NATO on Wednesday that it needed to be realistic about the chances of restoring a cooperative relationship with Moscow.

He cited Moscow's 2014 annexation of Crimea from Ukraine. Mattis said NATO needed to "negotiate from a position of strength".

That prompted a terse reply from Russia's Defense Minister Sergei Shoigu.

"Attempts to build a dialogue with Russia from a position of strength would be futile," he was quoted as saying by TASS news agency.

Mattis shot back: "I have no need to respond to the Russian statement at all."