The controversy over Novak Djokovic's Australian visa application has been "damaging on all fronts", the men's professional tennis tour has said.

Djokovic left an immigration detention hotel on Monday after his visa cancellation was overturned in court.

But Australia's immigration minister still has powers to re-cancel the visa and deport the unvaccinated player.

"Complications in recent days related to player entry into Australia have... highlighted the need for clearer understanding, communication and application of the rules," said an ATP statement.

"In travelling to Melbourne, it's clear Novak Djokovic believed he had been granted a necessary medical exemption in order to comply with entry regulations.

"The series of events leading to Monday's court hearing have been damaging on all fronts, including for Novak's well-being and preparation for the Australian Open."

Following his release, Serbia's Djokovic, 34, posted a photo of himself and his team - including coach Goran Ivanisevic - on court at the Rod Laver Arena in Melbourne, where he has won a record nine Australian Open men's singles titles.

This year's tournament begins on 17 January and if Djokovic wins, he will become the most successful men's player in history.

The world number one is tied with Switzerland's Roger Federer and Spain's Rafael Nadal on 20 Grand Slam singles titles.

Though Djokovic has not spoken publicly about his vaccination status, in his interview with border officials he confirms he is not vaccinated.

He told the interviewer that he tested positive for Covid twice - in June 2020 and on 16 December 2021. Copies of his positive PCR tests were provided to the interviewer - one was issued on the 16 December 2021, a day before Djokovic appeared at public events without a mask.

The ATP added: "More broadly, ATP continues to strongly recommend vaccination for all players on the ATP Tour, which we believe is essential for our sport to navigate the pandemic.

"This is based on scientific evidence supporting the health benefits provided and to comply with global travel regulations, which we anticipate will become stricter over time.

"We are encouraged that 97% of the top 100 players are vaccinated leading into this year's Australian Open."

Nadal called the build-up to the Australian Open a "circus".

"Justice has spoken and has said that he [Djokovic] has the right to participate in the Australian Open and I think it is the fairest decision," Nadal told the Spanish radio station Onda Cero.

Czech player Renata Voracova had her visa was cancelled after travelling to Australia.

The Czech government said Voracova entered Australia on a valid exemption. Like Djokovic, she had contracted Covid-19 recently.

The Australian government said on Friday that a recent infection does not mean a foreign national can travel to the country without being fully vaccinated.

"Hopefully he can play. Because that is what we went there for: to play tennis and not be part of any inside games," said Voracova.

'Djokovic is not able to relax yet' - analysis

Russell Fuller, BBC tennis correspondent

That late-night practice session at Melbourne Park must have been one of the most exhilarating of Novak Djokovic's career.

Having won an unexpected victory in an altogether different court earlier in the day - with the judge expressing sympathy for him throughout - his hopes of a 10th Australian Open title are still alive.

Australian Border Force suggested Djokovic brought little evidence into the country to support his medical exemption. Judge Kelly saw it completely differently, asking "what else could he possibly have done?"

But the world number one is not able to relax just yet, as the Australian immigration minister is expected to decide on Tuesday whether to use his personal power to cancel the visa for a second time.

And in the days ahead Djokovic will also need to justify why he posed for photographs with children at a prize-giving the day after his December positive PCR test was confirmed.