Rudd accused Turnbull of a breach of trust, saying he and Turnbull had been close since Rudd left the Prime Ministership in 2010 and Turnbull had appeared to support him going for the role, which they regularly discussed.
That changed in May this year when Turnbull said that support would not be forthcoming a month after Rudd first asked to be nominated. Rudd said he was stunned.
However, Foreign Minister Julie Bishop had then told Rudd to keep up with his campaign because she had brokered an arrangement with Turnbull to wait until after the election to take the matter to Cabinet.
There was no mention of Helen Clark in the article.
After Clark was nominated for the role by New Zealand Rudd had said she was a credible candidate but he firmly believed an Eastern European would get the job.
In the interview with The Australian, Rudd said he had no idea who would get the job which depended mainly on the five permanent members of the Security Council: Britain, China, France, Russia, and the US.
Last week 9News' political correspondent Laurie Oakes questioned whether Prime Minister John Key had a role in persuading Turnbull not to endorse Rudd after Key revealed he had discussed Clark's candidacy with Rudd several times, including in the days leading up to the Cabinet meeting.
Australia has not yet expressed support for any candidate, including Helen Clark.
Turnbull has said the Government would consider its position in coming weeks.
In an Essential poll in Australia in April, 45 per cent of Australians backed Clark over Rudd while just 21 per cent said they would back Rudd.
The Security Council will hold a second straw poll early Saturday morning, NZ-time.
The early straw polls are partly an attempt to narrow down the field of 12 candidates.
On Friday, the Croatia former Foreign Minister Vesna Pusic pulled out after coming bottom in the first straw poll.
She reportedly had just two votes in support and 11 discouraging.
Ban ki-Moon will step down at the end of this year after serving two terms.
The secretary-general is chosen by the 193 member General Assembly on the recommendation of the Security Council.