"The fundamental threshold point is this: does the government believe, do we believe, do I as Prime Minister believe Rudd is well suited for that role?" Turnbull told the media here, adding "My considered judgement is he is not".
The decision by Turnbull effectively crushed Rudd's hopes of nabbing the post after he spent months lobbying for government support.
Without the backing of the Turnbull government, Rudd, the former Prime Minister of the opposition centre-left Labour Party, cannot run for the next UN chief.
Rudd had hoped Australia's conservative government would take the crucial step of formally nominating him to succeed UN Secretary-General Ban Ki-moon when Ban's second five-year term ends on December 31.
A final nominee will not emerge before October once the UN Security Council offers its candidate to the General Assembly for consideration.
The Security Council is set to hold its second straw poll next week, which had strong support for former Portuguese Prime Minister Antonio Guterres.
There currently 12 contenders vying for the post, with six being female, and eight from Eastern Europe.
Australia will consider its position with respect to other candidates, including compromise contender, former New Zealand Prime Minister Helen Clark in due course, Turnbull added.
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