The Kentucky senator touted the letter earlier Wednesday morning, saying he was "honored to deliver a letter from President Trump to President Vladimir Putin's administration".
The White House told Fox News that Paul asked Trump to write a letter of introduction to the Russian leader.
Trump was widely criticized in the USA for his performance at the Helsinki summit as he appeared to embrace Putin's denial that Russia had interfered in the election, equating the Russian leader's stance with the US intelligence community's finding that Russia had sought to help Trump win.
The White House said the Republican president had provided Paul with a "letter of introduction" for his trip at the senator's request.
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".
China continues 'fair and lawful' business in Iran, despite US sanctions
The Trump tactics have deepened an already serious economic crisis in Iran, fuelling protests around the country. Turkey, however, said it would continue to buy natural gas from Iran.
Kremlin spokesman Dmitry Peskov said on Wednesday that a letter from Trump to Putin had been delivered by diplomatic channels, the Interfax news agency reported. In a joint news conference with Trump, Putin said he did want Trump to win because then-candidate Trump had said he wanted to improve U.S. But Peskov said the Kremlin had not familiarized itself with the contents.
The senator met with members of the Russian parliament's upper house who serve on the foreign affairs committee Monday. He also held talks in Moscow with parliamentarians and pledged to block new sanctions against Russian Federation. He (Paul) is interested in leglislative [sic] exchanges, parliamentary dialogue and cultural and educational exchange programs, increased counter-terrorism co-operation, 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.
Paul (R-Ky.) never secured a meeting with the Russian president.
Oil and gas. In the energy sector, the legislation would impose sanctions on investment in any projects by the Russian government or government-affiliated companies outside Russia worth more than $250 million.