"I do not believe Julia Gillard can lead the Australian Labor Party to success at the next election."
Mr Rudd said he would declared his position after arriving back in Australia and talking to colleagues.
He said he had spoken to colleagues overnight, who "regard me as the best prospect to lead the Australian Labor Party at the next election".
Mr Rudd expressed "contentment, happiness and surprise" at the level of support for him.
He was "shocked and disappointed at the tone of personal attacks launched against me overnight in Australia".
"I would urge my own supporters not to retaliate," he said, adding negative politics have no place in Australian Labor Party.
However he would not speculate whether he had the numbers in the caucus to topple Ms Gillard.
"Anyone is a mug who believes in circulated lists of numbers at this stage of a possible ballot process,'' he said.
"There is a huge doctrine of enlightened self-interest at work when people put out one list or another in terms of how many numbers people have.''
Mr Rudd said the question of the party's leadership was "not about personality, it's about trust, it's also about policy, it's about vision".
He said the party's achievements when he was leader were "formidable", including getting through the Global Financial Crisis without entering recession.
Then, with a gesture highly reminiscent of his time as prime minister, Mr Rudd ended the press conference to head for the airport for the trip back to Australia.
"Folks, as they say in the classics, I've gotta zip.''