"I have decided that at 10:00 am Monday (2300 GMT Sunday) a ballot for the Labor leadership will be conducted," Gillard told reporters.
She said the squabbling within the party must cease for the sake of the nation. "Australians are rightly sick of this and they want it brought to an end," Gillard was quoted as saying by The Australian newspaper.
Gillard said she "expects" to win but ruled out a future challenge if she lost, and asked Rudd to make a similar commitment.
"If I do not receive the support of my colleagues I want to make it clear that I will go to the back bench and renounce any leadership ambitions... I anticipate that Kevin Rudd will be a contender in the leadership ballot and I ask him to give the same undertakings that he will go to the back bench and renounce leadership ambitions."
Gillard accused her colleague Rudd of a "a long running destabilisation campaign" and, referring to damaging leaks against her, said the 2010 election "was sabotaged".
Earlier, Rudd resigned his post as foreign minister at a dramatic press conference in Washington and attacked Gillard-led government over its poor relations with business, and criticised a number of policy decisions made since he lost the prime ministership.
He was ousted as prime minister in a shock party-room coup in June 2010. Then his deputy, Gillard challenged Rudd and went on to take the prime ministership unopposed.
Rudd said Gillard could not win the next election and he would make an announcement on his intentions soon.