US President Donald Trump's Defence Secretary says he does not see the conditions for military collaboration with Russia, in a blow to Moscow's hopes of repairing ties with the United States following Mr Trump's election.

Key points: Rejection appears to close the door on joint military incursions with Russia

Rejection appears to close the door on joint military incursions with Russia Mattis says Russia interfered in democratic elections

Mattis says Russia interfered in democratic elections Russia's President has been calling for more cooperation with both the US and NATO

"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," James Mattis told reporters after talks at NATO headquarters in Brussels.

General Mattis' comments appeared to nullify repeated suggestions by Mr Trump during his election campaign of the possibility of joint action against Islamic State militants.

His blunt rejection came after Russian President Vladimir Putin called for increased intelligence cooperation with the US and NATO, and it makes such coordination less likely at least in the near future.

General Mattis followed his dismissal with a sharp assessment of Russia's alleged election meddling, saying there was "very little doubt that they have either interfered or they have attempted to interfere in a number of elections in the democracies".

His comments raised questions about the Trump administration's policies towards Russia.

As a candidate, Mr Trump repeatedly praised Mr Putin, saying he wanted a new era of cooperation with Moscow.

Ties between Mr Trump's team and Russia came under the spotlight this week, with the resignation of national security adviser Michael Flynn.

Mr Flynn resigned after disclosures he had discussed US sanctions on Russia with the Russian ambassador to the United States before Mr Trump took office, and that he later misled Vice-President Mike Pence about the conversations.

Speaking at a meeting of NATO defence ministers, General Mattis said the US would continue to engage politically with Mr Putin's government to try to find common ground.

He said political leaders would seek "a way forward where Russia, living up to its commitments, will return to a partnership of sorts here with NATO".

"But Russia is going to have to prove itself first," he added.

Defence ministers from the NATO countries gathered in Brussels for the meeting. ( ABC News: Niall Lenihan )

The US ceased military-to-military relations with Russia in the wake of Moscow's 2014 annexation of Ukraine's Crimea region.

But last year, the Obama administration considered plans to cooperate militarily with Russia as part of a ceasefire deal in Syria.

Senior Defence Department leaders opposed the plan, and it quickly fell apart as the ceasefire collapsed.

Russian Foreign Minister meets US counterpart

In a separate meeting, Secretary of State Rex Tillerson and Russian Foreign Minister Sergey Lavrov made the highest-level face-to-face contact between the two countries since Mr Trump took office.

The men met on the sidelines of a G20 foreign ministers meeting in Bonn, Germany.

Reporters were present during Mr Lavrov's opening remarks to Mr Tillerson, the former CEO of Exxon Mobil Corp, but were quickly ushered out when the US Secretary of State began to speak.

Mr Lavrov was asked whether Russia was concerned about turmoil in the Trump administration.

"You should know we do not interfere in the domestic matters of other countries," he said.

He said his meeting with Mr Tillerson had addressed conflicts in Syria, Ukraine and Afghanistan, but not US economic sanctions on Russia.

"The meeting was pragmatic, business-like," Mr Lavrov said. "We noted the existence of common interests, primarily in terms of the fight against terrorism."

AP/Reuters