"This is judgment about Mr Rudd's suitability for that particular role.
"The threshold question here when the Australian Government nominates the person for a job, particularly an international job like this, is do we believe the person...is well suited for that position.
"My judgment is that Mr Rudd is not."
He had explained the reasons why to Rudd but he would not go into them. He did not want to add to his disappointment.
He had spoken to Rudd only just in the past hour.
Asked if the Australian Government would now support Helen Clark, he said that was yet to be considered.
The UN Security Council has held one secret ballot and is due to hold a second one on August 5.
Clark was placed sixth out of the 12, though Foreign Minister Murray McCully said it was a "marathon, not a sprint."
Rudd was not expected to have been a top contender.
But having him in the contest would not have helped Clark and could have drawn claims of a divided Pacific.
Rudd, a former diplomat and Mandarin speaker, was a polarizing politician and has attracted polarising views about whether he should get Government backing.
Former New South Wales Labor Premier Kristina Keneally said last week she could think of 12 Australian who would be a better secretary general "and one of them is my labrador."
But Acting Labor leader Tanya Plibersek said that Rudd was well qualified and that a rejection of him would be small-minded and wrong.
Rudd was elected Prime Minister in 2007 but was deposed before his term was finished by colleagues who found his management style chaotic.
He served as foreign minister in Julia Gillard's Government but ousted her three months before the 2013 election which he then lost.
New Zealand Prime Minister John Key said this week that he did not believe an entry by Rudd into the contest would make much difference. In a "drag race" between Clark and Rudd he knew which one would win and it would not be Rudd.
Clark is up against those countries who believe the appointment should be rotated on a geographic basis and that it is Eastern Europe's turn but many countries believe it is time for a woman to head the UN.
The Tony Abbott Government pledged to support Clark but that was before Rudd formally sought the support of the Australian Government.
Public hearings have been held by the UN General Assembly where Clark was widely judged to be a top performer.
Under UN rules, the General Assembly must approve the final selection after a recommendation from the Security Council.
After the first ballot, the candidates ahead of Clark were Antonio Guterres of Portugal, Danilo Turk of Slovenia, Irina Bokova of Bulgaria, Vuk Jeremic of Serbia and Srgjan Kerim of Macedonia.
Behind her were Miroslav Lajcak of Slovakia, Susanna Malcorra of Argentina, Christiana Figueres of Coast Rica, Natalia Gherman of Moldova, Igor Luksic of Montenegro, and Vesna Pusic of Croatia.
Ban Ki Moon completes two terms as Secretary General on December 31.
Rudd issued a statement tonight as follows:
"Mr Rudd thanks Foreign Minister Bishop, and her many Cabinet colleagues for their consideration of and support for his candidacy for United Nations Secretary General.
"It would have been the first time in the United Nation's 70 year history that Australia offered a candidate for UN Secretary General.
"It would have reflected well on what our nation can offer to the world - as a middle power with relationships across the world, including the developing world, smaller states, the Commonwealth, our Pacific Island friends and of course our partners in Asia.
"Mr Rudd requested to be considered as a former Prime Minister, a former Foreign Minister, a career diplomat, as someone who successfully campaigned for an Australian position on the UN Security Council in 2013-14, and who has chaired the Independent Commission on Multilateralism, a two year long review of the UN system against the core question of whether the UN remains fit for purpose.
"A nomination by the government would not have granted Mr Rudd a position. It would simply have enabled him to stand alongside the 12 other candidates from across the world, and compete on his merits.
"That is now not to be.
"Mr Rudd flew to Sydney this morning requesting a meeting with the Prime Minister, having sought such a meeting the previous evening.
"On arrival in Sydney Mr Turnbull telephoned Mr Rudd, indicating there was no opportunity for a meeting.
"Mr Turnbull stated he would not be nominating Mr Rudd as a candidate for UN Secretary General.
"It is a pity the Government has not seen fit to support him, as the Hawke Government supported Malcolm Fraser for the post of Secretary General of the Commonwealth, or the Howard Government supported Gareth Evans to be head of UNESCO.
"Mr Rudd wishes well all candidates for the position of UN Secretary General.
"Mr Rudd remains a fervent defender and advocate of the UN in these difficult times. We need the UN now more than ever."
