Later, Mr Rudd referred to her remarks when asked if he would challenge Ms Gillard.
"That is not in prospect, because we have a prime minister and I am the foreign minister," he told reporters.
Mr Rudd's apparent climbdown comes after a weekend in which persons unknown released a video on the online portal YouTube of the then-prime minister swearing and banging a table in frustration while trying to record a message.
It's not clear when the footage was recorded, but it was before Mr Rudd was rolled by Ms Gillard in June 2010 amid MP complaints about his leadership style and the government's decline in the polls.
The video release heightened expectations Mr Rudd would soon challenge Ms Gillard, who is herself presiding over poor polling for Labor.
Rudd supporters told AAP on Monday they have mustered 30 votes in the caucus - well short of the 52 needed for a win.
Backers of the prime minister dispute this figure, saying Mr Rudd more likely has 20 votes, against Ms Gillard's support base of around 50. A further 20 to 30 are undecided.
One senior Labor source said it was in neither Mr Rudd nor Ms Gillard's interest to have a leadership vote next week.
"If Rudd gets 30, that kills her in the long term," the MP said.
"Her best strategy is to ignore the elephant in the room.
"Kevin's best tactic is to wait. He is picking people up ... and will keep picking up people."
He said many of those who currently back the prime minister have set her an August 2012 deadline - after a budget surplus and carbon tax compensation are delivered - to improve the party's stocks or face a challenge.
On Monday, cabinet minister Simon Crean again went into bat for the prime minister, saying Mr Rudd was not a team player.
Mr Rudd said he was disappointed by Mr Crean's remarks because "they are based on an untruth" that he had raised the leadership issue with independent MP Andrew Wilkie last November.
"Can I say with absolute clarity, at no stage during that conversation - or any other conversation - have I sought anyone's support for any concern on that matter as far as the leadership is concerned," Mr Rudd said.
Mr Wilkie concurred, saying he had raised the issue when chatting with Mr Rudd about other matters and at no stage did the foreign minister ask for his support.
However, Mr Crean warned Labor was in danger of "mutual destruction" if the leadership question was left unresolved.
Queensland Labor backbencher Graham Perrett repeated his threat to quit if Ms Gillard was dumped, which would trigger a by-election in his seat of Moreton that could threaten the government.
On Monday, he used Twitter to reinforce his message: "Looking fwd (sic) to a late election campaign in 2013 with PM Julia Gillard out front of a great Labor record and team".
Meanwhile, former Queensland premier Peter Beattie says the speculation is killing Labor's chance of retaining government in the state election on March 24.
"It's time that there was a caucus meeting and the matter was dealt with once and for all," he said.
- AAP
