Labor’s political opponents have united behind the Coalition to order Anthony Albanese to hand over official documents regarding “melon” comments the prime minister made in a crude podcast interview about a gift from the Japanese prime minister.

NSW Premier Chris Minns interrupted persistent questioning of Albanese at a press conference on Thursday following a week of negative coverage about the saga. The prime minister has refused to apologise, leaning on a statement from the Japanese ambassador on Wednesday that sought to downplay its significance, in a rare public intervention after the gaffe was reported in Japanese media.

The Greens and independent senator David Pocock lamented the distraction, but united with the Senate crossbench and opposition on Thursday to ensure further scrutiny. They backed Liberal senator James Paterson’s demand for the government to produce by Monday the diplomatic cables from Japan, as well as internal texts, emails or handwritten notes about the gaffe from Albanese’s office.

The Coalition referred the matter of the leaked diplomatic cable to the Australian Federal Police on Tuesday, and it hopes internal communications will reveal the source of the leak.

Paterson said: “It’s not often the Coalition, the Greens, David Pocock and One Nation agree on something. No one believes Albanese’s denials. I don’t even think he does.”

The controversy over the prime minister’s appearance on the Bush Deep podcast has only gained momentum after Albanese was initially forced to apologise for saying he wanted to “shag” pop darling Kylie Minogue.

Asked on the podcast about gifts he had received as prime minister, Albanese referred to the “couple of melons” Japanese prime minister Sanae Takaichi brought when she visited in May, gesturing with his hands in front of his chest. Host Nikki Osborne replied: “She just came in looking like Pamela Anderson.”

Opposition Leader Angus Taylor seized on the comments this week, saying Albanese disrespected the leader of one of Australia’s key trading partners and should apologise.

Minns, who has had a frosty relationship with the prime minister, interrupted persistent questions about the comments at a press conference on Thursday, where their governments were announcing a $2.5 billion bailout for the Tomago aluminium smelter.

“Go and ask 1000 workers what they care about today,” Minns said, interrupting the prime minister as he was repeating that he had had a warm dinner with Takaichi when they met in May.

“This is the biggest announcement for this region in a generation, can we just talk about it for five minutes?” Minns said.

Greens leader Larissa Waters said her party had backed the call for the documents to be released in the interest of transparency, but slammed the Coalition for blowing the saga out of proportion.

“The prime minister did the wrong thing here. So, as a matter of transparency, we generally support documents being disclosed,” she told ABC’s Afternoon Briefing.

Pocock also lamented the distraction and that the prime minister had not resolved the issue with an apology.

“I think how you deal with mistakes says a lot about your character as a leader,” Pocock said.

Orders for production of documents are a crucial tool of the Senate to enable it to scrutinise the government. Labor senators voted against Paterson’s move, but were outnumbered. The government will be forced to provide an explanation to the upper house if it does not meet the Monday deadline.

The Coalition led question time on Thursday by attacking the prime minister over the “classless comments”.

“Why won’t the prime minister man up, stop hiding behind his colleagues, and take responsibility for his grubby behaviour?” Taylor asked before Albanese pointed to the Japanese ambassador’s statement from Wednesday that said the leaders’ meeting in May built trust between the nations.

“We have a very good relationship with Japan,” Albanese said. “I look forward to continuing to work with our friends on economic issues as well as interests of peace and security and prosperity in our region.”

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Brittany Busch is a federal politics reporter for The Age and Sydney Morning Herald.Connect via email.