Two senior Opposition MPs have asked the Australian Federal Police to investigate if and how confidential correspondence between the Japanese Prime Minister’s office and Anthony Albanese was leaked to Australian media outlets.

It comes after Mr Albanese on Tuesday rejected assertions he had insulted Sanae Takaichi for references to the female leader’s “melons”, as he resisted growing calls to apologise for the comments made during a controversial podcast.

During his now infamous appearance on the Deep Bush podcast in July, the Prime Minister said he would “shag” popstar Kylie Minogue and joined in on jokes about the Japanese leader “smuggling” two prized crown melons into the country.

On Monday evening reports emerged of a diplomatic cable dated July 13, sent by the Japanese government, which “noted” the “sensationalised reporting in the Australian media” about Mr Albanese’s comments in an interview with podcaster Nikki Osborne.

The diplomatic note, reportedly sent to the Department of Prime Minister and Cabinet in Canberra, stated that Tokyo’s belief was that there was no “ill intention” in Mr Albanese’s appearance on the podcast.

According to The Australian there was also an undertaking to take “no action” over the incident and that no public response from Japan would assist the Albanese Government because it would “allow the Australian media to move on”.

A separate report by Seven News quoted a letter from the Japanese Prime Minister sent to Mr Albanese expressing “heartfelt gratitude for Australia’s profound friendship” following a recent earthquake.

Shadow Minister for Defence James Paterson and former Liberal Party deputy leader Ted O’Brien have put their request in writing to AFP Commissioner Krissy Barrett, saying a deliberate leak could constitute a criminal offence.

Their letter, obtained by The West Australian, said it was “critically important” Australia’s bilateral partners could trust confidential correspondence would be handled appropriately.

“We write to refer the possibly unlawful disclosure of confidential and sensitive correspondence from the Government of Japan to the Department of Prime Minister and Cabinet,” it said.

“We are concerned that a diplomatic note with a critical bilateral partner has potentially been provided to the media without authorisation . . . it is possible that this disclosure is a criminal offence under Division 122 of the Commonwealth Criminal Code.

“It is critically important that Australia’s bilateral partners believe that their confidential correspondence will be handled appropriately by the Australian government.

“It would be gravely damaging to our national interest if they formed the view the Australian Government does not take unauthorised disclosure seriously by promptly investigating it.”

The Opposition questioned both the Prime Minister and Foreign Affairs Minister Penny Wong about the growing scandal when Parliament returned on Tuesday.

“Do you know how the media obtained this sensitive diplomatic correspondence,” Senator Paterson asked Senator Wong during Question Time.

“In relation to what you have raised, I have seen those reports publicly. I don’t know what correspondence is being referred to,” Senator Wong replied.

Senator Paterson then pressed Senator Wong on whether the Government would investigate “how confidential correspondence from one of our closest and most important partners to the Department of Prime Minister and Cabinet was leaked to the media?”

After Senator Wong insisted the Government enjoyed a “very close and trusting relationship with the Government of Japan”, Senator Paterson again went on the attack.

“Minister, isn’t it true that in a desperate attempt to clean up the Prime Minister’s self-inflicted melon mess, the Government is now risking a critical bilateral relationship by leaking confidential correspondence?” he asked.

“Wouldn’t it be easier for the Prime Minister to just admit he got it wrong and say sorry?”

At the same time in the House of Representatives, Liberal MP Mary Aldred asked the Prime Minister if he would “personally apologise” to the Japanese leader for his “disrespectful behaviour” on the Bush Deep podcast.

“I reject the assertion in the question,” Mr Albanese said in response.

He added that he and Ms Takaichi were “friends” which had been displayed in her recent visit to Canberra, when she had gifted him the melons.

“Australia and Japan have never been closer or more strategic, and my government has taken our special strategic partnership to new heights,” he said.

After weeks of headlines in Australia, The controversy is now also being reported in Japan, with the Asahi Shimbun newspaper carrying an article titled: “the Australian Prime Minister allegedly made sexually suggestive remarks regarding melons gifted by Takaichi”.

Earlier on Tuesday, several of Mr Albanese’s colleagues were again forced to defend their leader’s appearance on the podcast, including Agriculture Minister Julie Collins and Environment Minister Murray Watt.

On at least six occasions the pair were questioned about Mr Albanese’s Japanese crown melons joke with both brushing off the assertion that the PM’s remarks and actions, which included a cupped hand gesture in front of his chest, were sexual in nature.

“I know the Prime Minister very well, and the Prime Minister’s been very clear that the type of inference that you’re applying there is not what he was (intending),” Ms Collins said

Minister Watt was then pressed by journalists on why the PM didn’t defend the female foreign leader against podcast host Nikki Osborne’s crude joke — which compared her gifted edible melons to Pamela Anderson’s breasts.

“Is it appropriate, though, for a man to let a crude joke like that go by without saying anything, without standing up to the woman involved,” one reporter asked.

Senator Watt again said: “We’ve been clear that any statements or the Prime Minister’s participation in that part of that episode has been misinterpreted”.