Paul, an ally of Trump, said he had travelled to the Russian capital to encourage diplomacy amid tense relations between Moscow and Washington.
In addition, Putin in Helsinki allegedly spoke with trump about the new ban the deployment of weapons in outer space and called for the establishment of a consultative mechanism at the level of Ministers of defence and foreign Affairs.
"My goal in coming to Russian Federation is to say that we want to have open lines of communication", Paul said at a press conference after the meeting.
"At Senator Paul's request, President Trump provided a letter of introduction", deputy press secretary Hogan Gidley said, adding that Trump in the letter "mentioned topics of interest that Senator Paul wanted to discuss with President Putin".
Paul has been one of the president's most vocal defenders in recent weeks, defending Trump for appearing to accept Putin's denials of US election interference.
The Trump administration has prepared an eight-page draft of an executive order that would allow the White House to sanction non-United States citizens for meddling in US elections.
But Peskov said the Kremlin had not familiarized itself with the contents.
Paul remained supportive of Trump following the US President's performance during a news conference with Putin in July.
The tweet set off a flurry of speculation, given the controversy sparked by a Trump-Putin summit in Helsinki last month.
The president later corrected some of his remarks, saying he misspoke.
He also held talks in Moscow with parliamentarians and pledged to block new sanctions against Russian Federation. "He is interested in legislative exchanges, parliamentary dialogue and cultural and educational exchange programs, increased counter-terrorism cooperation, building on recent successes like the disruption of the St. Petersburg plot and resolution of the military conflicts in Syria and Ukraine".
The relationship has also created divisions within the administration.
It is also the latest example of Paul making overtures to Russian officials that are out of step with congressional GOP leaders, who have not blessed his visit. Under pressure from Congress, which a year ago passed a tough sanctions law targeting Russia, the U.S. Treasury in April imposed sanctions on Russian officials and oligarchs for election meddling and "malign" activities.
A reported text of the draft bill published Wednesday sent Russia's ruble to lows against the dollar last seen in April.