Lavrov added that any meeting with US Secretary of State Mike Pompeo would have to take place after the summit in Helsinki.
Peskov said that President Putin "and Russian Federation are open for dialogue and jointly searching for compromises", TASS reported.
Trump met individually with North Korean leader Kim Jong Un and their translators during the June 12 summit in Singapore before their entourages joined in, the report said, and wants to repeat that experience with Putin.
Lavrov, speaking in English, said he hoped that the U.S. senators' visit "will symbolise the resumption of relations between the (US and Russian) parliaments".
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Describing the concert hall as "iconic", Macron said that "we have to build a new common narrative" in Africa. President Macron pointed out that only Nigerians could change their image before the comity of nations.
Asked about whether the visiting USA lawmakers would meet Putin, Peskov said: "For now, it is not on the president's schedule, but we know that the American officials have planned quite wide-reaching contacts with their colleagues".
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 United States record may be kept.
Russian Foreign Minister Sergey Lavrov, back to a camera, listens to U.S. Sen.
He said the Kremlin was "very satisfied" that the senators were visiting Russian Federation. "Indeed, we do not rule out that both Presidents Putin and Trump may have a tête-à-tête meeting at the beginning, if an initial agreement is confirmed and there is preliminary understanding".