Djokovic announced the positive tests as part of a statement Tuesday:
"We organized the tournament at the moment when the virus has weakened, believing that the conditions for hosting the Tour had been met. Unfortunately, this virus is still present, and it is a new reality that we are still learning to cope and live with.
"I am hoping things will ease with time so we can all resume lives the way they were. I am extremely sorry for each individual case of infection. I hope that it will not complicate anyone’s health situation and that everyone will be fine.
"I will remain in self-isolation for the next 14 days, and repeat the test in five days."
Djokovic later addressed the matter further and noted his children have tested negative for the virus:
Djokovic has received criticism for the event, in which several top players took part in other activities such as basketball and dancing without following social-distancing guidelines.
Grigor Dimitrov, Borna Coric and Viktor Troicki are among the other players who took part in the tournament and have since tested positive for the coronavirus.
Christopher Clarey @christophclarey
Undefeated in 2020 before the pandemic shut down the tour, Novak Djokovic is hardly on a winning streak anymore. His no-distancing Adria Tour looks like folly at this stage. My latest with input from many in the game: https://t.co/WDnzRmQJaF https://t.co/fTgkro3cCm
Pictures from the tournament showed not only players in close contact but also fans in the stadium with few protective face coverings:
"Boneheaded decision to go ahead with the 'exhibition,'" fellow ATP Tour player Nick Kyrgios wrote on Twitter. "Speedy recovery fellas, but that's what happens when you disregard all protocols. This IS NOT A JOKE."
The ATP Tour is scheduled to resume with the Citi Open in Washington, D.C., on Aug. 14. It's one of two warm-up events slated to take place before the U.S. Open begins Aug. 31. The French Open is set to take place starting Sept. 27.
Play has been halted since March 12 because of the coronavirus pandemic. Wimbledon was canceled in April, leaving this year's schedule with three major tournaments.
Djokovic, who won the Australian Open in February, is a 17-time Grand Slam singles champion.
Bleacher Report's David Gardner interviews athletes and other sports figures for the podcast How to Survive Without Sports.