Paul said that members of the Foreign Affairs Committee of the upper house of the Russian parliament, the Federation Council, had been invited "to come to the United States to meet with us in Washington."
"I think this is incredibly important," the US lawmaker was quoted as saying in translated comments by Interfax news agency.
The "main aim of the trip" was to "create a dialogue" and "improve relations" between Moscow and Washington, Paul added.
US President Donald Trump has come under fire for failing to challenge Vladimir Putin over election meddling at their summit in Helsinki last month. And Paul is the only Republican lawmaker to stand by Trump during that controversy.
The head of the Federation Council's foreign affairs committee, Konstantin Kosachev, suggested that a meeting in Washington might take place "as early as during the fall session, that is, before the end of this year".
He said he saw the current trip by US senators to Moscow as "especially valuable when other American politicians are making efforts to portray any contact with Russian politicians as toxic".
Kosachev dismissed new accusations that Russia had meddled in US elections.
"There was no meddling in 2016. Certainly it will not happen during the ongoing election campaign either," he said.
"During a conversation the two sides exchanged views on current issues of bilateral relations, as well as some aspects of arms control," the Russian foreign ministry said in a statement.
It added that "special attention was given to the possibility of developing inter-parliamentary contacts".
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