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Immigration Minister Alex Hawke is weighing exercising his discretionary powers to revoke Djokovic's visa which could scuttle his bid for a record 21st major tennis title at the Open.
The official draw was due to start at 3pm (local time), but after a short delay, a tournament staffer told reporters outside the media conference room it would not go ahead.
Djokovic, a vaccine sceptic, fuelled widespread anger in Australia last week when he announced he was heading to Melbourne for the Australian Open with a medical exemption to requirements for visitors to be inoculated against Covid-19.
When Djokovic arrived, Australian Border Force officials decided his exemption was invalid and he was held alongside asylum-seekers at an immigration detention hotel for several days.
A court on Monday allowed him to stay on the grounds that officials had been "unreasonable" in the way they handled his interview in a seven-hour process in the middle of the night.
The 34-year-old world number one was out practicing on Rod Laver Arena earlier on Thursday.
The Australian government, which has won strong support at home for its tough stance on border security before and during the pandemic, must now decide whether to let Djokovic remain and bid for a 10th Australian Open title.
Djokovic's cause was not helped by a mistake in his entry declaration, where the box stating he had not travelled abroad in the two weeks prior to leaving for Australia was ticked.
In fact, he had gone to Spain from Serbia.
Djokovic attributed the error to his agent and acknowledged he also should have rescheduled an interview and photoshoot for a French newspaper on Dec. 18 while infected with Covid-19.
Fans, including many Serbian Australians, gave him noisy support when he was detained, anti-vaxxers have hailed him as a hero and his family have portrayed him as a champion for individual rights.
But Djokovic may face hostility from the crowd when he walks out on court.
There is widespread anger over the saga among Australians, who have a 90% vaccination rate among adults and are battling a wave of the Omicron variant after enduring some of the world's longest lockdowns aimed at curbing the pandemic.
"I don't like his arrogance," Teyhan Ismain, a Melbourne resident, said on Wednesday. "It does seem that he's been telling a few fibs too. So I think he should just probably go back."
There may also be resentment in the dressing room, where all but three of the top 100 men are inoculated.