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Morrison's comments contradicted those of his immigration minister Alex Hawke, who said last week that tennis players and other athletes would have to be double vaccinated to enter the country.
The Prime Minister's statement is good news for Tennis Australia, who want Serbia's world No 1 Novak Djokovic and other top players whose vaccination status is unclear to be able to compete at the Grand Slam.
"All the same rules have to apply to everyone," Morrison told Seven News on Wednesday.
"Whether you're a Grand Slam winner, a prime minister or a business traveller, a student or whoever. Same rules. The states will set the rules about the quarantine as they are."
The state of Victoria, where the Melbourne Park venue of the tournament is situated, will almost certainly enforce the quarantine regulations to the strictest extent.
Victoria's Premier Daniel Andrews is vehemently opposed to letting unvaccinated people into the country but said on Tuesday the state would "manage the risk" if the federal government decided to allow it.
Djokovic has declined to disclose his vaccination status and said last week he might not play at the tournament "things being as they are".
The policy shift is likely to prove controversial in Victoria, which has grimly endured six lockdowns since the start of the global health crisis.
Professional athletes in the state are under a vaccine mandate, which also covers coaches, officials, media and other staff involved in elite competition.
That means tennis players might well be the only unvaccinated cohort at the Australian Open, where ballkids, fans and umpires will need proof of vaccination.
Tournament organiser Craig Tiley had heralded the policy change in discussions with the men's ATP and women's WTA tours last week.
Currently around 70% of the top 100 men and women players are vaccinated.
For the last edition of the tournament in February, Tennis Australia spent tens of millions of dollars on biosecurity, including putting Djokovic and other elite players in luxury accommodation in Adelaide to serve their quarantine period.
If Djokovic decides to go to Australia, he will be favourite to win a record 21st men's singles Grand Slam title - moving him out of a tie with Roger Federer and Rafa Nadal.
An "abundance of caution" has been Australia's mantra through the pandemic with the country's borders effectively sealed for 18 months.
Melbourne, the country's second-largest city and host of the Australian Open, has been locked down six times.
The sixth lockdown ended last Friday but only for the vaccinated 70% of adults. The unvaccinated remain banned from sporting events, bars and restaurants, and could remain so well into 2022.