Mr Peters called Mr Carr "nothing more than a Chinese puppet" and more on Radio NZ on Thursday morning.
New Zealand is debating involvement in pillar two of the military tie-up, which will see AUKUS members - Australia, the UK and US - developing and sharing advanced warfaring technologies with other nations.
Mr Carr shared his criticisms of the US-led pact on a visit to Wellington in April, calling it "methane-wrapped bulls**t" and saying he admired Kiwi foreign policy as it wasn't as "gullible to the Americans" as Australia.
On Wednesday night, Mr Peters gave a major foreign policy speech at parliament, where he said NZ was yet to consider collaboration on pillar two as it had not been invited.
Mr Peters followed up with a round of interviews on Thursday morning where he was asked about Mr Carr's criticism, launching an extraordinary broadside.
"What on earth does he think he's doing walking into our country and telling us what to do? We would no more do that in Australia than he should do here. That's the kind of arrogance we don't like," Mr Peters told Radio NZ.
Bob Carr shared his criticisms of the US-led pact on a visit to Wellington in April. (Ben McKay/AAP PHOTOS)
Mr Peters called Mr Carr "nothing more than a Chinese puppet", before suggesting even further alignment in comments AAP has chosen not to republish.
Radio NZ has also edited an uploaded clip of the interview to remove the potentially defamatory remarks.
AAP understands Mr Carr, who is in Europe and unavailable for comment, intends to bring defamation action.
Former NZ prime minister Helen Clark, who spoke alongside Ms Carr at the Labour-aligned anti-AUKUS conference in April, told Radio NZ Mr Peters had "seriously defamed" Mr Carr.
Former New Zealand prime minister Helen Clark believes Bob Carr has been defamed by Winston Peters. (Ben McKay/AAP PHOTOS)
The spat has roused Opposition Leader Chris Hipkins to call for Mr Peters' sacking as deputy prime minister and foreign minister.
"Winston Peters has once again embarrassed New Zealand by making potentially defamatory allegations about a senior and respected leader from our closest ally," he wrote on social media.
"The prime minister needs to show some leadership and stand him down immediately."
Prime Minister Chris Luxon is yet to respond to the call, but will not do so, given his coalition government is built off Mr Peters' support.
Mr Luxon leads a three-party coalition, with Mr Peters leading junior partner NZ First.
Mr Peters is not the first to question Mr Carr's links to Beijing.
Mr Carr led the Australia China Relations Institute at the University of Technology in Sydney after taking office.
Speaking to AAP in Wellington in April, he insisted he was not blind to China's misdeeds.
"Australia is entitled to challenge China, to press back against China's influence-building in the South Pacific," Mr Carr said.
"I've criticised China for militarising artificial structures in the South China Sea. I believe the extinction of legal autonomy for Hong Kong was wrong.
"I've always said Australia and other partners of China are entitled to press human rights and make specific reference to Tibet and Xinjiang province and the Uyghurs.
"No one's ever advocating that we not talk about deterrence, where it's required to maintain an honourable balance of power in Asia.
"But I've made very clear my reservations about AUKUS. $368 billion is the biggest transfer of wealth outside of Australia that has ever happened in our history."
