According to RIA Novosti, citing a source in the Association of Tennis Professionals (ATP), the players had to do this under the threat of a ban on the tour.
On March 1, ATP decided to allow Russian tennis players to participate in tournaments only in a neutral status.
A similar decision was made by the Women's Tennis Association (WTA).
Medvedev is the first racket of the world, and Khachanov is ranked 25th in the ATP rankings.
Earlier it was reported that Khachanov, following Medvedev, removed the Russian flag from his Instagram profile.