Putin's spokesman, Dmitry Peskov, said the Kremlin has not yet examined the letter Paul presented.
"We expect that in the nearest time it will come to the presidential administration," Peskov said, according to Russian news agencies.
The White House did not comment immediately on the letter or its contents.
Paul said on Twitter that "the letter emphasized the importance of further engagement in various areas, including countering terrorism, enhancing legislative dialogue and resuming cultural exchanges."
The Kentucky Republican met with members of the Russian parliament's upper house who serve on the foreign affairs committee Monday. Paul said he had invited them to Washington.
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