"The President hopes that a meeting can help reduce tensions", US Ambassador to Russia Jon Huntsman told reporters on a briefing call set up by the White House.
The meeting, to be held in Helsinki on July 16, is the first major summit between the two leaders and comes as relations between Moscow and Washington have sunk to levels not seen since the Cold War. "We have to be vocal about it, on guard about it", said Francis.
Trump is slated to meet Putin in Helsinki on July 16.
Lavrov, speaking in English, said he hoped that the United States senators' visit "will symbolize the resumption of relations between the (US and Russian) parliaments".
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Some have criticised Trump's approach to speaking privately with world leaders - which one former official called a "threat to national security" - and have raised concerns that discussions may get lost in translation and that no formal USA record may be kept.
"I am here not to accuse Russia of anything, I am here to try to find ways to improve relations", Shelby told Russian lawmakers, according to a transcript published on the Duma website. The U.S., alongside the European Union, placed tough economic sanctions on Russian Federation in response.
"We have a strained relationship, but we could have a better relationship between he USA and Russian Federation, because there's some common interests around the world that we hopefully can work together on", Shelby said, according to video from the meeting in Moscow.
Trump has expressed scorn for the alliance and is expected to upbraid European NATO members for not spending enough on their own defense.
However, he took issue with President Trump's statement that he planned to discuss Crimea with President Putin there.