At least one topic of discussion appears off the table for President Donald Trump's upcoming summit with Russian President Vladimir Putin: Russia's 2014 annexation of Crimea from Ukraine.
US-Russian relations have plummeted in recent years amid Russia's involvement in the Ukraine crisis and allegations that Russia meddled in the 2016 US presidential election.
"We recognise that the world is better off, I believe, if Russia and the U.S. have fewer tensions, get along a little better, maybe put aside some differences", Senator Richard Shelby said during Tuesday's meeting with Lavrov at the Russian foreign ministry.
Russian Foreign Minister Sergey Lavrov, left, listens to U.S. Sen.
For the second day in a row he stressed that the two powers do not necessarily need to be adversaries, but competitors like in sports or trade.
The US delegation is in Russian Federation until Thursday, ahead of the summit planned in Helsinki on July 16, at a time of high tension between Russian Federation and the West.
The U.S. has been strongly opposed to Russia's actions in Crimea.
"I think the resumption of the inter-parliamentary dialogue is very timely in the run-up to the Helsinki meeting between the two presidents due in two weeks", Russia's top diplomat said.
Kremlin spokesman Dmitry Peskov said there was no plan for the senators to meet Putin.
Most recently, the USA leader angered European leaders when he reportedly suggested last month that he may be willing to reverse US policy and recognize Russia's 2014 annexation of Crimea from neighboring Ukraine.
He said the Kremlin was "very satisfied" that the senators were visiting Russian Federation.
For his part, Trump has left open the question of changing the US position on Crimea.
Russian-backed troops seized control of the region in 2014, and later held a referendum on becoming a part of Russia that was heavily criticized by the global community.