Elina Svitolina and Kiki Bertens withdraw from US Open

"After long consideration I have decided not to go to the States for Cincinnati and the US Open," the 28-year-old Bertens said on Instagram.

"The situation around Covid-19 is still worrying and the health of everyone and the control over this virus is priority."

The United States has close to 5 million cases of Covid-19 and almost 160,000 people have died, according to a Reuters tally.

The US Open organisers are creating a bio-secure 'bubble' in New York to hold the tournament from August 31 without spectators. But concerns remain about players and their team members being able to travel outside that bubble during the tournament fortnight, and whether players would face mandatory quarantines upon returning home from the US Open.

"Our prime minister indicated yesterday that we should be quarantined for 14 days after coming back from the States," Bertens said.

"Of course we respect this as a team and this would disturb our preparation for my beloved clay court tournaments in Rome and Paris. I hope the situation will soon take a positive turn and wish everyone good health."

The Italian Open is scheduled to be held in Rome from September 20 ahead of the French Open Grand Slam in Paris a week later.

Shortly afterwards, Ukrainian Svitolina announced that she would not be going to New York either.

She wrote on social media: "I understand and respect all the efforts they are putting to make it happen in a safe environment, but I still don't feel comfortable to travel to US without putting my team and myself at high risk."

Tournament organisers said when they announced the initial entry list that nine of the world's top ten women were expected to be in Flushing Meadows, but that seemed an optimistic prediction, with many of them based outside the USA and thus requiring significant travel.

Men's defending champion Rafa Nadal and women's world number one Ashleigh Barty have also opted against travelling to New York to play the hardcourt Grand Slam as well as the Western & Southern Open that will work as a warm-up for the US Open.