Russian Foreign Minister Sergei Lavrov described the talks in Reykjavik on Wednesday -- aimed in part at confirming a potential summit between presidents Biden and Vladimir Putin -- as "constructive".

"There is an understanding of the need to overcome the unhealthy situation in ties between Moscow and Washington," Lavrov told reporters, although he added there were "a lot of logjams".

During almost two hours of discussions, US Secretary of State Antony Blinken expressed Washington's "deep concerns" about Russian troops massed along the Ukraine border despite an announced pullback, a US State Department spokesman said.

Blinken also voiced US disquiet over the health of jailed Kremlin critic Alexei Navalny and the "repression" of opposition organisations, the spokesman added.

While there was no breakthrough, discussions were "productive, constructive, respectful and honest", a US official told journalists.

Since taking over the White House in January, Biden has taken a firm line against Russia -- going as far as describing Putin as a "killer" -- in sharp contrast to his predecessor, Donald Trump, who was accused of complacency towards the Russian leader.

At the start of the talks, Blinken said "our view is that if the leaders of Russia and the United States can work together cooperatively ... the world can be a safer and more secure place".

"But if Russia acts aggressively against us, our partners, our allies, we will respond," he warned, reiterating that Washington wants a "predictable and stable" relationship with Moscow.

"We are ready to discuss all issues without exception if we understand that discussions will be honest and based on mutual trust," Lavrov responded.

- Arctic tensions -

Statements before the face-to-face talks on the sidelines of the Arctic Council meeting in Iceland did not appear to bode well for a de-escalation of tensions.

Blinken had called for the Arctic to become a laboratory for cooperation focused on common challenges such as the fight against global warming.

But Lavrov issued a strongly worded warning on Monday.

"It has been absolutely clear for everyone for a long time that this is our territory, this is our land," Lavrov said at a press conference in Moscow.

The Russian foreign minister at the same time accused Norway of "trying to justify the need for NATO to come into the Arctic".

He insisted Russian military activity in the region was "absolutely legal".

The Russian warning prompted Blinken on Tuesday to stress that Washington wanted to "avoid a militarisation" of the Arctic.

"We have concerns about some of the increased military activities in the Arctic. That increases the dangers or prospects of accidents," Blinken said.

- 'Plough through the rubble' -

There were some signs of thawing relations just before the meeting when the White House announced it would not sanction the main company involved in the Nord Stream 2 gas pipeline project between Russia and Germany, Nord Stream AG, and its managing director.

Sanctions are still planned against some entities, but the Biden administration wants to avoid antagonising Berlin and in doing so has cleared a major obstacle for the pipeline to go ahead.

Meanwhile, Lavrov stressed the need for "building and maintaining bridges and dialogue", and said he was ready to "plough through the rubble left over from previous US administrations".

One priority was to ensure the proper functioning of US and Russian diplomatic missions, currently reduced to minimum service following tit-for-tat expulsions of diplomats.

Biden and Putin have agreed in principle to hold their first summit, possibly in June in Europe following a G7 summit and a NATO leaders' meeting.

On Monday, Blinken said he expected the summit to happen in the next few weeks.

But asked after the meeting if Russia had formally agreed to the summit, Lavrov did not reply.

He said he had reiterated Moscow's suggestion of beginning broad dialogue with the United States on strategic stability and that Blinken did not object.

"But experts will have yet to work on it," he added.