The three Trump supporters said they were comfortable with the widely panned display from the USA president, and proceeded to clash with the dissenters.
Trump has pushed for easing tensions between the former Cold War foes, exacerbated by USA intelligence findings that Russian Federation meddled in the 2016 presidential election, trying to tilt the outcome to Trump.
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.
"I was honored to deliver a letter from President Trump to President Vladimir Putin's administration", Paul tweeted.
Paul, an ally of Trump, said he had traveled to the Russian capital to encourage diplomacy amid tense relations between Moscow and Washington.
The letter comes three weeks after Trump met with Putin in Helsinki, Finland, sparking a backlash in both parties after his initial refusal to side with the US intelligence community over Russian denials about meddling in the 2016 presidential election.
Paul remained supportive of Trump following the US President's performance during a news conference with Putin in July.
According to Russian state news agency RIA Novosti, Putin's press secretary Dmitry Peskov confirmed that the letter was sent to Putin "through diplomatic channels", but the Kremlin has not yet reviewed it.
But earlier this week, Paul extended an invitation to Russian lawmakers to visit Washington, D.C., in an effort to prompt exchanges between the two countries' parliamentary bodies.
Senators are mulling legislation to slap new sanctions on Russian Federation.