Mr Rudd's request to be officially nominated by the government was discussed in a lengthy and polarised cabinet meeting in Canberra on Thursday, in which ministers shared their views on the former Labor leader's suitability for the prestigious role.

Cabinet resolved to hand responsibility to Mr Turnbull alone, who said he would communicate the decision to Mr Rudd in a phone call to Brisbane.

After weeks of speculation and resistance from senior Coalition members, Foreign Minister Julie Bishop was expected to argue for Mr Rudd's suitability, while his nomination was opposed by some senior ministers, including Scott Morrison and Peter Dutton.

Labor and the Greens had called on the government to support Mr Rudd, citing support for former Australian prime ministers including Malcolm Fraser, in bids for international roles.

Mr Turnbull would not discuss the decision at a press conference at Parliament House.

"We've considered this issue and I owe Mr Rudd a telephone call before I say anything more about it publicly," he said.

Any further delay could have potentially thrown Mr Rudd's bid into doubt as consideration of candidates by UN member nations gets under way next month.

Social Services Minister Christian Porter also declined to discuss the decision on Thursday.

"I know that you are compelled to ask, but we have seen the Prime Minister say that he's making a phone call and of course they're matters that I will leave to the Prime Minister," he said.

Earlier, Greens leader Richard Di Natale said Australia not supporting the nomination would be "churlish and mean-spirited".

Ms Bishop, the main backer of Mr Rudd in cabinet, recently told the Coalition partyroom that a "nomination is not an endorsement" but Mr Turnbull said it would amount to indirect support.

Mr Morrison, Mr Dutton, Industry Minister Greg Hunt and several government backbench MPs have publicly questioned his merit and suitability to be secretary-general.

Acting Opposition Leader Tanya Plibersek said a failure to nominate Mr Rudd for partisan reasons would be "small-minded" and embarrassing for Australia.

"I I don't think I can imagine anyone who is better qualified for this job than Kevin Rudd," she said.

"He was a distinguished former prime minster of Australia, a very successful foreign minister... with decades' worth of diplomatic experience.

"He's acknowledged in the United States as an expert on China and Asia more generally. His skill is acknowledged around the world."

Former Coalition minister Eric Abetz said Labor figures have called Mr Rudd a narcissist, micro-manager, impulsive control freak and psychopath and that "these are not qualities listed on the job-ad for UN chief".

There is global momentum for a woman to become secretary-general for the first time, while eastern European nations believe they are due to have a representative in the top job.

Of the 12 declared candidates, Antonio Guterres, former prime minister of Portugal, is considered a frontrunner after a strong showing in the first straw poll vote.

Former New Zealand prime minister Helen Clark has the backing of her country's government, but is believed to have lost some momentum from the unofficial straw poll.

The next secretary-general will take office on January 1.

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