"The letter was received through diplomatic channels. We expect it to be received by the presidential administration soon," Peskov said.
Earlier in the day, US Sen. Rand Paul said he delivered a letter from Trump to Putin's administration.
"I was honored to deliver a letter from President Trump to President Vladimir Putin's administration. The letter emphasized the importance of further engagement in various areas including countering terrorism, enhancing legislative dialogue and resuming cultural exchanges," Paul said in a Twitter message.
The Trump administration, as well as the Kremlin, has not yet commented on the issue.
The visit follows US President Donald Trump and Russian President Vladimir Putin's Helsinki summit, held on July 16, which effectively relaunched a dialogue between the two countries after a long period of tension.