US Secretary of State Rex Tillerson on Thursday told his Russian counterpart Sergei Lavrov that Washington would cooperate with Moscow but only if it was in Americas and its allies interest to do so.

"The United States will consider working with Russia when we can find areas of practical cooperation that will benefit the American people," Tillerson said after his first meeting as secretary of state with Lavrov.

"Where we do not see eye to eye the United States will stand up for the interests and values of America and her allies," he said on the sidelines of a G20 foreign ministers gathering in Bonn.

Tillerson also urged Russia to meet its Minsk ceasefire commitments in Ukraine, where Russian intervention and its annexation of Crimea have plunged ties with Moscow into a deep freeze.

All eyes were on Tillerson as he made his debut as America's top diplomat after President Donald Trump promised to put US interests first while also offering a softer line on Moscow.

The meeting with Lavrov took place as Washington reels from the shock resignation of national security adviser Michael Flynn over contacts with Moscow's ambassador and allegations of Russian meddling in Trump's election last year.

For his part, Lavrov told Tillerson that Moscow does not interfere in other countries' internal affairs.

"You should know we do not interfere in the domestic matters of other countries," Lavrov told reporters.

"We have plenty of issues to discuss... I believe that we can discuss and establish the parameters of our future work," he added.

Tillerson, who up to now has been notably tightlipped with the press, reportedly said: "Thank you Mr Lavrov, it's a pleasure to see you."

Earlier, President Vladimir Putin called for restoring links between US and Russian intelligence agencies to face common problems such as terrorism.

Trump has said previously he would be open to anti-terror cooperation with Russia.