MELBOURNE, Australia — Novak Djokovic, the top-ranked men’s tennis player, acknowledged on Wednesday that a travel document he presented to Australian border officials last week contained false information, as the country’s authorities continued to investigate whether he should be deported.

Mr. Djokovic also said that he had participated in an interview and a photo shoot last month in his native Serbia even after testing positive for the coronavirus, in an apparent breach of the country’s rules for infected people. Australian officials have said they are looking into whether Mr. Djokovic, who is unvaccinated, poses a risk to public health.

The tennis star’s comments came in a statement he released on social media that he said was intended to “clarify misinformation” about the weeks before he arrived in Melbourne for the Australian Open. He was detained for days by Australian border officials before being ordered released on Monday by a federal judge.

But Mr. Djokovic’s statement did not fully resolve a range of questions that have swirled over his quest to remain in Australia and seek a record 21st Grand Slam title. Among them are exactly when he learned of the positive test result and how his travel documents came to falsely assert that he had not traveled internationally in the 14 days before his arrival in Australia.

The statement posted on Instagram, which Mr. Djokovic said would be his last remarks about his ordeal in Australia, was released as the country’s immigration minister said he was still considering whether to exercise his personal powers to cancel the player’s visa again. Immigration officials were also investigating the discrepancies in the paperwork Mr. Djokovic presented as he tried to enter Australia last week with an exemption from a requirement for Covid-19 vaccinations.

Australian tennis officials granted that exemption on the basis of what Mr. Djokovic had said was a Covid infection he had in mid-December. He had come under criticism over images on social media showing him at events at the same time he was supposedly infected with the coronavirus.

Mr. Djokovic said on Wednesday that he had taken a P.C.R. test on Dec. 16 after some people at a basketball game he had attended two days earlier tested positive for the coronavirus. Despite having no symptoms, he also took a rapid antigen test “out of an abundance of caution,” he said, and it came back negative.

On Dec. 17, he said, as he was awaiting his P.C.R. result, he attended a tennis event in Belgrade, the Serbian capital, where he presented awards to children. He said that he took another rapid antigen test before attending that event, which came back negative, and that his P.C.R. test did not come back positive until after it had finished.

On Dec. 18, he went ahead with an interview and a photo shoot with the French sports newspaper L’Equipe “to fulfill a longstanding commitment,” he said.

“I felt obliged to go ahead and conduct the L’Equipe interview as I didn’t want to let the journalist down, but did ensure I socially distanced and wore a mask except when my photograph was taken,” Mr. Djokovic said.

“While I went home after the interview to isolate for the required period, on reflection, this was an error of judgment and I accept that I should have rescheduled this commitment,” he added.

It was not the first time Mr. Djokovic has had to apologize for dismissive actions he has taken during the pandemic. In mid-2020, as the virus raged in Europe and elsewhere, he held a tennis tournament after which he and several others tested positive.

While Mr. Djokovic said in his statement on Wednesday that he “had not received the notification of a positive PCR result” until Dec. 17 — after the event involving children — documents he provided to Australian officials as he tried to enter the country said that the result had been returned the day before.

A copy of his medical certificate for his positive P.C.R. test said that the test was taken at 1:05 p.m. on Dec. 16 and that the positive result was returned at 8:19 on the same day. In an affidavit provided to an Australian court, he said, “On 16 December 2021, I was tested and diagnosed with SARS-CoV-2 (COVID).” It was unclear when exactly he learned of his purported positive test.

The Serbian prime minister, Ana Brnabic, said this week that had Mr. Djokovic known that he was positive for the coronavirus before attending the awards event on Dec. 17, he would have “clearly violated the rules” in Serbia.

But more information was required, she added, saying, “I don’t know when he received the test result, when he read it.”

When asked what would happen if Mr. Djokovic was found to have breached quarantine rules, she said the Serbian government would “deal with it.”

In his statement, Mr. Djokovic also addressed questions about the declaration he made on his visa paperwork that he had not traveled to any other countries in the 14 days before arriving in Australia. The paperwork warns of serious penalties for false answers to the question.

His declaration had seemed to be contradicted by social media posts showing him traveling between Spain and Serbia. On Wednesday, he said his agent had made an “administrative mistake in ticking the incorrect box.”

“This was a human error and certainly not deliberate,” he said, adding that his team on Wednesday had “provided additional information to the Australian government to clarify the matter.”

This means it is unlikely that the saga will be resolved quickly, with the immigration minister, Alex Hawke, indicating that he needed more time to consider the new information before deciding whether to cancel Mr. Djokovic’s visa again.

A spokesman for Mr. Hawke said that Mr. Djokovic’s lawyers had made “lengthy further submissions and supporting documentation said to be relevant to the possible cancellation of Mr. Djokovic’s visa.”

“Naturally, this will affect the time frame for a decision,” he added.