"I was honored to deliver a letter from President Donald J. Trump to President Vladimir Putin's administration", Sen.
Paul described the letter from Trump as a correspondence that "emphasized the importance of further engagement in various areas including countering terrorism, enhancing legislative dialogue and resuming cultural exchanges".
The meeting last month was also attended by the Russian Foreign Ministry and a USA delegation led by Thomas Pickering, former Undersecretary of State.
A White House official told CNN that Paul wanted this letter from Trump in hopes of setting up a meeting with Putin during his trip to Moscow this week.
The two had savaged each other on the 2016 presidential primary campaign trail, with Paul at one point deriding Trump as an "orange-faced windbag" and the president retorting that Paul was "truly weird".
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At the time, uncertainty about what Mr Trump and Mr Putin discussed during the private meeting in which members of the press were also banished from caused a stir.
Paul is not the first USA lawmaker to visit Russian Federation in recent weeks: last month, eight congressional Republicans traveled to Moscow and met with high-ranking officials, including senior members of Russia's parliament and the foreign minister, Sergey Lavrov.
Last week, Trump's national security team said Russian Federation is behind "pervasive" attempts to interfere in the November midterm elections, in a rejection of denials of meddling that Putin made directly to Trump. Paul said he had invited them to Washington. Facing public pressure, including criticism from some Republicans, Trump later said he misspoke.