Liberal Leader Angus Taylor, whose party has referred a media leak of a memo from Tokyo over the matter to federal police, interrupted parliamentary proceedings on Wednesday to demand that a formal apology be made to Japan Prime Minister Sanae Takaichi.
The controversy has its origins in Mr Albanese's appearance on the Bush Deep podcast that aired in July, when he mentioned Ms Takaichi had gifted crown melons to him during a recent visit to Australia.
"She brought two, and they're beautiful," he said in the podcast, in which he made controversial hand gestures.
Mr Taylor slammed the comments, saying they were wrong to women and to a close political partner.
"Even if they were a gaffe, they were wrong and there are serious consequences from the unserious podcast that the prime minister hosted in the Lodge," he said.
He also asked the prime minister to explain how correspondence about the gaffe sent from Japan was leaked.
Media coverage over the comments in both countries prompted a letter from Tokyo to Canberra, which said there had been ''sensationalised reporting in the Australian media'' about the interview. It was allegedly leaked to several outlets.
No action would be taken by the Japanese government over the incident, it reportedly said.
Mr Albanese's comments largely escaped scrutiny when the podcast was published, but they were later picked up by Japanese papers, before Australian media ran coverage.
The coalition's foreign affairs spokesperson Ted O'Brien and his colleague, Senator James Paterson, this week wrote to Australian Federal Police commissioner Krissy Barrett and requested an investigation into how the leak occurred.
''It is critically important that Australia's bilateral partners believe that their confidential correspondence will be handled appropriately by the Australian government," the letter said.
Mr O'Brien told reporters on Wednesday that "Japan is a special strategic partner of Australia and this has to be taken seriously. Trust is the currency of diplomacy."
Housing Minister Clare O'Neil responded to news of the coalition's probe calls by saying the Liberals had "absolutely lost the plot".
"My personal view is that the Australian Federal Police should be allowed to focus on their job, which is keeping Australians safe and fighting crime for Australians," she told Seven's Sunrise.
Senator Paterson on Wednesday accused the government of having a "short memory", given Labor Senator Katy Gallagher referred leaked correspondence between the then-coalition government and French Prime Minister Emmanuel Macron to the AFP several years ago.
"Labor can't have it both ways. It's either always wrong for confidential communications from our allies to find their way into the media, or it's wrong only when their political opponents do it," he said.
The melons themselves, which AAP confirmed were valued at $400, fell under the expense threshold for reporting so were not recorded on the prime minister's official gift log.
Still, on Wednesday, One Nation Leader Pauline Hanson demanded that Mr Albanese declare the melons on his register of interests. The precise number of melons gifted was of concern, she said.
"Now we're hearing he had four melons, and he ate two, and then he realised. Now he says he's got four. He's always lied to the public," Senator Hanson told reporters.
