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US Secretary of State Rex Tillerson made his diplomatic debut at a G20 gathering in Germany on Thursday as Russia pressed the Trump administration to keep its promises of improved relations.

All eyes were on Tillerson as he held initial talks with his British, Saudi and UAE counterparts.

America's top diplomat also met Russian Foreign Minister Sergei Lavrov as controversy raged over Trump's possible ties to the Kremlin and the shock resignation of his national security advisor Michael Flynn over contacts with Russia.

Tillerson said on Thursday that the US was ready to work with Russia if there were common areas for cooperation, but said Moscow had to adhere to commitments made over Ukraine.

"As we search for new common ground we expect Russia to honour its commitment to the Minsk agreements and work to de-escalate violence in Ukraine," Tillerson told reporters after meeting with his Russian counterpart Sergei Lavrov.

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

"Even a simple exchange of information about the channels and sources of terrorists, about people implicated in or suspected of terrorism seriously raises the effectiveness of our joint efforts," Putin told the country's FSB intelligence agency in a televised speech.

On the campaign trail, Trump said he would be open to anti-terror cooperation with Russia.

Separately, US Defense Secretary James Mattis said in Brussels that Washington was not ready "right now" for military collaboration with Russia.

Several US investigations are under way into alleged meddling by Russian intelligence services in favor of Trump during last year's elections, charges the president has angrily dismissed as nonsense.

Tillerson is a former head of US oil giant ExxonMobil reputed for making major deals in Russia and having close enough ties to Putin to merit a top Russian honor.

Host nation Germany billed the two-day G20 meeting as a chance for the club of leading and developing economies to discuss how to work together on challenges ranging from climate change to conflicts in Syria, Ukraine and Yemen.

The Texan could also face questions about the Israeli-Palestinian conflict, after Trump caused international consternation Wednesday by dropping Washington's years-long quest for a two-state solution, saying he would back a single state if it led to peace.

Tillerson is part of a major US diplomatic offensive after Trump caused dismay in Europe by dubbing NATO "obsolete," praising Brexit, claiming the EU is doomed and taking a distinctly softer line on Russia.

US Defence Secretary James Mattis is attending the second day of a NATO meeting in Brussels on Thursday, while Vice President Mike Pence was the highest-ranking US official participating in the Munich Security Conference.

"There are plenty of uncertainties about what they want, what they plan," a European diplomat said about the Trump administration. "We hope we'll get some clarity in the weeks to come."

Initially, Mattis had taken a more conventional line than President Trump but his blunt words Wednesday came as a shock.

Pence has likewise used more moderate language than his boss but his visit to Europe this week will be closely watched to see if he has a similarly hardline message to deliver.

The G20 meeting is being hosted by German Foreign Minister Sigmar Gabriel who has been a vocal critic of Trump's protectionist and nationalist leanings.

The G20 countries account for some 85 percent of the global economy and two thirds of the population.