"I was honored to deliver a letter from President Trump to President Vladimir Putin's administration", the Kentucky Republican announced on Twitter. He says the letter emphasized the importance of working together on counter-terrorism, legislative talks and cultural exchanges.
Paul was an enthusiastic supporter of Trump's decision to meet with Putin in the first place, writing that "dialogue is especially important when hundreds of millions of lives are at stake, as is the case in relations between the United States and nuclear-armed Russian Federation".
After the summit, Paul and Trump discussed the senator's planned meetings with Russian officials and the messages the president wanted Paul to convey to them. But no new meeting has been scheduled and the White House said it was delaying a Putin visit to Washington until 2019, by which time it said it expects special counsel Robert Mueller's criminal investigation into Russian meddling in the 2016 US presidential election to be completed.
Paul, who is in Russia this week for meetings with top Russian officials, has emerged as a key ally for Trump in his campaign for warmer relations with Moscow.
The White House had no immediate comment on the letter.
The president has called an investigation into possible ties between his campaign and Moscow a "witch hunt", but his administration has warned that the threat of meddling from Russian Federation endures.
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.
A U.S. official provided to CNN the text of the letter, which read: "I would like to introduce Senator Rand Paul of Kentucky, a member of the Senate Foreign Relations Committee, and a voice for expanding dialogue with the Russian Federation. He also invited a delegation of Russian lawmakers to Washington DC.
The relationship has also created divisions within the administration.
There has been no indication that a Putin-Paul meeting will take place.
Paul's colleagues in the Senate from both parties introduced legislation last week to impose strict new sanctions on Russian Federation.