Novak Djokovic said the mistake on his immigration form about travel prior to arriving for the Australian Open was an "administrative error".
The men's tennis world number one he had not travelled in the two-week period before his flight to Australia.
However, Djokovic was filmed playing tennis in the streets of Belgrade in Serbia on Christmas Day and training in Spain on 31 December, both within the 14-day window.
His statement said: "On the issue of my travel declaration, this was submitted by my support team on my behalf - as I told immigration officials on my arrival - and my agent sincerely apologises for the administrative mistake in ticking the incorrect box about my previous travel before coming to Australia.
"This was a human error and certainly not deliberate."
The statement, posted to Instagram, also covered what he called "continuing misinformation" about attendance at events in December "in the lead up to my positive PCR COVID test result".
He tested positive for COVID-19 in December but added: "I want to emphasise that I have tried very hard to ensure the safety of everyone and my compliance with testing obligations."
Djokovic said he took a rapid antigen test on 16 December after attending a basketball game two days previously where people attended who went on to test positive.
This test came back negative, and a day later he tested negative again on a RAT and attended an event in Belgrade where he presented awards to children.
Djokovic wrote that he only got a positive test - through PCR - after that event and went to a tennis centre to conduct an interview with a French sports newspaper on 18 December - "as I didn't want to let the journalist down" - and isolated after this.
"While I went home after the interview to isolate for the required period, on reflection, this was an error of judgement and I accept that I should have rescheduled this commitment," he added.
Meanwhile, a decision on Djokovic's future in Australia is unlikely to come on Wednesday after his lawyers "provided lengthy submissions" to Immigration Minister Alex Hawke.
Mr Hawke could still use his ministerial powers to remove the world number one from Australia despite the Serbian having the cancellation of his visa quashed earlier this week by a ruling of the Federal Circuit Court.
Should such a discretionary decision be made, Djokovic could be banned from entering the country for three years.
Mr Djokovic's lawyers have recently provided lengthy further submissions and supporting documentation said to be relevant to the possible cancellation of Mr Djokovic’s visa," a spokesman for Minister Hawke said.
"Naturally, this will affect the timeframe for a decision."
His mother Dijana Djokovic told the Seven Network on Wednesday she doesn't "think it's fair" that Minister Hawke could still use personal powers to remove the tennis world number one from the country - a move he is still considering.
Dijana said she was "very worried" her son could meet such a fate, and acknowledge the saga is "not over".
“I am praying that he will stay and he will play. I hope that everybody is thinking the same. I hope the government and the minister is thinking (the same)," she told the Seven Network.
“Don’t throw him out. He is a tennis player. He is not a politician. He is not a criminal. He is not a murderer. He is just a tennis player, the best in the world. Just let him play and show what he knows.”
Prime Minister Scott Morrison is dealing with the possibility of a diplomatic fallout should Djokovic be deported ahead of the Australian Open.
Mr Morrison held talks with his Serbian counterpart Ana Brnabic on Tuesday, where the prime minister explained Australia's border policy.
The leaders agreed to stay in contact on the issue and to further strengthen the bilateral relationship between the countries.
Victorian Premier Daniel Andrews said the Australian Open was bigger than one player.
However, he said he was not lobbying the immigration minister to act in a certain way on the matter.
"I'm not going to be out there every day calling for him to use (discretionary powers) or not use them, that's a matter for him," Mr Andrews said.
"He ought to do that free of any pressure, free of any public debate."
Following the court's decision, Djokovic practised on Rod Laver Arena late on Monday night, and again on Tuesday.