World number five Elina Svitolina and world number seven Kiki Bertens have become the latest players to pull out of the US Open.
In a statement, Ukraine’s Svitolina, a semi-finalist last year, said she did not feel comfortable travelling to the US “without putting her team and herself at high risk”.
Bertens, from the Netherlands, pulled out because of Dutch government regulations that require people returning from the United States to quarantine for two weeks.
The 28-year-old said that would disturb preparations for her “beloved clay court tournaments”.
Australia’s world number one Ashleigh Barty is the only other women’s top 20 player to have withdrawn so far, although number two Simona Halep, from Romania, is not expected to play either.
Men’s world number two Rafael Nadal has not entered, and his great rival Roger Federer is absent recovering from injury, but world number one Novak Djokovic is on the entry list.
The tournament is scheduled to begin on 31 August and will be played without fans.