The announcement follows days of mutual accusations from authorities in Kyiv and Moscow over delays in the exchange of their fallen soldiers.
Neither Russian nor Ukrainian officials confirmed the exchange.
Putin called the over-two-hour-long conversation "meaningful, frank and very useful."
The ship, Green Admire, was leaving Sillamae port using a designated navigation channel that crosses Russian territorial waters.
The 909 fallen soldiers were said to have died on the front lines in the Donetsk, Luhansk, Zaporizhzhia, Kharkiv and Sumy regions.
Kyiv had not reported any drone attacks since the Russian truce came into effect, but it did accuse Moscow of hundreds violations.