Prime Minister Malcolm Turnbull has accused Kevin Rudd of releasing accounts of conversations and meetings "at odds with my recollection" and which in one particular case was "absolutely untrue".
In the latest round of the escalating row over the government's refusal to nominate Mr Rudd for the position of United Nations secretary general, Mr Turnbull said he had advised him in May he was unlikely to gain cabinet support.
He said Mr Rudd had always known this would be a matter for cabinet.
Mr Rudd has claimed Mr Turnbull expressed support for his nomination at a meeting on December 23 last year.
"That is absolutely untrue. That meeting was held in my office with my chief of staff and it was made very clear to him that it was a matter for the cabinet," Mr Turnbull told ABC Radio.
Mr Turnbull said he had seen the correspondence Mr Rudd has "leaked or released" which included letters from Mr Rudd to Mr Turnbull.
"They include accounts of conversations and meetings that are at odds with my recollection," he said.
He said he and Mr Rudd held discussions of this topic over a long period of time. These were all private conversations, he said.
"It says a lot about Mr Rudd that quite some time after the event, he would seek to present an account of them in correspondence he would write to me with the clear intention of subsequently releasing it," he said.
Media reports suggest the Department of Foreign Affairs and Trade backed Mr Rudd but Mr Turnbull retorted: "You should not make that assumption at all."
"The fundamental issue here is one of substance - does the government believe Mr Rudd is well suited to the role. The answer is we do not and that is why we have not nominated him," he said.
Meanwhile, a former Australian ambassador to China who served under the Rudd and Gillard government, Geoff Raby, says Mr Rudd's bid could be far from over.
Mr Raby pointed out Mr Rudd was close to US Democratic presidential candidate Hillary Clinton.
In an opinion piece for the Australian Financial Review he speculated on the possibility of Mrs Clinton backing him for the job, if she wins the US election.
Treasurer Scott Morrison said the most important issue in Australia was not Kevin Rudd.
"The prime minister had expressed his reservations and opposition to this in the strongest possible terms in May so I don't think the outcome should have been a surprise," he told Sydney radio 2GB.
