Kevin Rudd

It comes in the wake of Prime Minister Malcolm Turnbull's decision not to nominate him to run for the UN's top job of secretary-general.

Mr Rudd argued the UN writes too many reports and has rigid institutional silos.

He also offered prescriptions, including that the UN prioritise field operations over head office and better include women.

The former prime minister addressed a Young Labor function in Brisbane on Saturday, a day after being told the Federal Government would not endorse his bid to become the next secretary-general.

He said it was part of the "collective scar-tissue" of life.

"Sometimes, it will turn to shit," he said.

Mr Rudd released the letters on Friday night, after Mr Turnbull revealed he had decided not to nominate him for the role as the world's top-ranking diplomat.

In the three letters, dated earlier this year, Mr Rudd wrote that Mr Turnbull had previously told him he would support his bid.

Mr Rudd made a last-minute dash to Sydney this morning in the hope of lobbying Mr Turnbull to nominate him as secretary-general of the United Nations.

But on arrival the Prime Minister called him and said the Government would not be backing him.

On Friday evening a spokeswoman for Mr Rudd released three letters which Mr Rudd had sent to Mr Turnbull about the issue.

In a Cabinet meeting that went well over time on Thursday, Mr Rudd's case was pushed by Foreign Minister Julie Bishop and supported by Attorney-General George Brandis.

The backing of some other ministers who spoke in favour has been described as lukewarm.

But many spoke against nominating Mr Rudd, including Immigration Minister Peter Dutton, Treasurer Scott Morrison and Finance Minister Mathias Cormann, who argued he was unfit for the role.

In the end it was left to the Prime Minister to make the call with the undertaking the leadership will support his decision.

It brings to an end months of speculation over Mr Rudd's bid for the role, currently held by Ban Ki-Moon.

Mr Ban's successor will take office on January 1, 2017.

Ms Bishop said it would be a matter for the Cabinet.

"Kevin Rudd has requested that the Australian Government nominate him and, as the Prime Minister has indicated on a number of occasions, that'll be a matter for Cabinet," she told Sky News.

According to RNZI, Australian foreign minister Julie Bishop said Mr Rudd had asked the federal government to nominate him.

The announcement brings to an end months of speculation over Mr Rudd's bid for the role, currently held by Ban Ki-Moon.

Ten candidates including former New Zealand prime minister Helen Clark are already vying to replace Ban Ki-moon when he steps down at the end of the year.