Svitolina stated in a statement that she feels that she cannot travel to the USA without putting her team and without putting herself in great danger.
Bertens withdrew due to restrictions imposed by the Dutch government, according to which those returning from the United States must be quarantined for two weeks.
Among the top 20 players, Ashleigh Barty, the world leader, withdrew from the American competition.
Simona Halep may also choose not to attend the US Open. She has not yet made a decision on this tournament but said that under the current conditions it will most likely not go to the US.
The US Open is scheduled for August 31-September 13, with no spectators and a strict sanitary protocol. There will be no qualifications for this grand slam.