Coric beat Dimitrov in the Croatian leg of the Adria Tour on Saturday, with the latter also appearing in Serbia last week, coming into contact with top 10 players Novak Djokovic, Alexander Zverev and Dominic Thiem.
Andrey Rublev, who was set to play Sunday's Zadar final against Djokovic before it was cancelled, confirmed later on Monday that he tested negative for COVID-19.
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Dimitrov returned home to Monaco after feeling unwell during his loss to Coric, and both have now returned positive coronavirus tests.
Coric confirmed his positive test on Instagram, writing: "Hi everyone, I wanted to inform you all that I tested positive for COVID-19. I want to make sure anyone who has been in contact with me during the last few days gets tested! I am really sorry for any harm I might have caused! I'm feeling well and don't have any symptoms [sic]. Please stay safe and healthy! Lots of love to all!"
A statement from Adria Tour claimed they followed all safety measures after Sunday's cancellation.
The statement from Sunday read: "As a precaution and to protect the health of all participants and visitors, the organisers of Adria Team have decided to cancel the grand finale of the tennis spectacle planned for tonight.
"At all times we have strictly followed the epidemiological measures in place with the countries where the Adria Tour was organised. None of the people involved in the organisation and who have been in contact with Grigor have any symptoms. However, we are in close contact with health authorities to insure that all people who were in contact with Grigor Dimitrov will be tested tonight."
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"I want to reach out and let my fans and friends know that I tested positive back in Monaco for Covid-19," Dimitrov wrote on Instagram on Sunday.
"I want to make sure anyone who has been in contact with me during these past days gets tested and takes the necessary precautions.
"I am so sorry for any harm I might have caused. I am back home now and recovering. Thanks for your support and please stay safe and healthy."
Dimitrov was filmed dancing in a nightclub with Djokovic, Zverev and others after last week's Adria Tour event in Belgrade, while he also joined his Zadar co-stars for a game of basketball on Thursday.
With international tennis suspended due to the COVID-19 pandemic, men's world number one Djokovic organised the Adria Tour as a charity event designated to be contested over four legs across the former Yugoslavia.
Austria's Thiem won the opening leg in Belgrade, where a capacity 4,000 crowd turned up on each day at Djokovic's tennis centre by the Danube river.
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With both Serbia and Croatia easing lockdown measures weeks before the event, players were not obliged to observe social distancing rules in either country and were seen embracing at the net at the end of their matches.
Fans in Croatia, however, were subject to the rules and had to keep their distance, meaning that the 9,000-capacity Visnjik tennis complex was half-full for the event.
The third leg due in Montenegro on June 27 and 28 was scrapped last week over coronavirus concerns while the final leg, scheduled for July 3 and 4 in Bosnia's Banja Luka, is now likely to be called off.
Djokovic's brother Djordje, the director of the entire Adria Tour series, said everyone who has been in contact with Dimitrov would be tested for COVID-19 in the next few hours.
"After receiving the news, we took all the measures stipulated by the Croatian government and everyone who has had any contact with Grigor will be tested," he said in a courtside interview.