(CNN) -- Australian Prime Minister Julia Gillard attempted Thursday to thwart a perceived challenge to her leadership of the Labor Party from former Prime Minister Kevin Rudd by announcing that she will put the matter to a vote of Labor members of Parliament on Monday morning.
"For far too long, we have been squabbling within the Labor Party, which has obscured the government's achievements and what we are doing to build a stronger and fairer Australia," she told reporters in Adelaide. "In recent days, I believe that this has moved to a distraction from governing itself. That's not good enough. Australians are rightly sick of this, and they want it brought to an end."
If she loses, she said, "then I will go to the back bench and I will renounce any further ambition for the Labor leadership." She called on Rudd to make a comparable commitment.
Her announcement ends months of speculation about a challenge to her leadership by Rudd, whom she replaced as prime minister in 2010. "I believe it is in the interests of the Labor Party that it be determined once and for all," she said.
Gillard's announcement appeared to have been sparked by Rudd's resignation on Wednesday, while visiting Washington, as Gillard's foreign minister. Before departing to return to Australia, he said, "I do not believe that Prime Minister Gillard can lead the Australian Labor Party to success in the next election."
Gillard rejected that assertion. "I believe I can lead Labor to that victory, provided that the Labor Party unites and we get on to the job."
Australia's next election has to be held by the end of November 2013.
And Gillard said Rudd's resignation means one thing: "It is now absolutely evident that Kevin Rudd is intending to return to Australia to ask me for a leadership ballot. I am not prepared for the nation to go through many days of drift before there is a clear point where this is going to be resolved."
The Australian media had been abuzz in recent days with reports that Rudd was considering contesting Gillard's leadership of the governing party.
Observers had predicted a showdown could take place next week when Parliament resumes. But Rudd's announcement in Washington in the middle of the night caught people by surprise.
"We thought he was tucked up in bed," said Angela Cox, a reporter for the Australian Channel 7 in the United States. "He called this late press conference, so we knew something must've been up. But I have to say most of us were pretty shocked when he actually said he was resigning as foreign minister."
This is not the first time the two senior Labor figures have clashed; Gillard became Australia's first female prime minister when she ousted Rudd from the Labor Party leadership in 2010 after he lost support within the party.
Tension between them in recent weeks has boiled over into newspaper columns and criticism from other party officials.
"There have been lots of calls for the prime minister, Julia Gillard, to sack him because he's been accused of disloyalty because of all of this speculation that he's doing backroom deals trying to challenge Julia Gillard for the leadership," Cox said. "He did say he felt compelled to do it today because he felt like he didn't have the support of Julia Gillard."
In a statement Wednesday, Gillard called Rudd "a strong and effective advocate for Australia's interests overseas" and said he "strongly pursued Australia's interests in the world."
"I am disappointed that the concerns Mr. Rudd has publicly expressed this evening were never personally raised with me, nor did he contact me to discuss his resignation prior to his decision," she said.
Rudd is considered responsible for bringing the Labor Party back from the wilderness. A Mandarin-speaking career diplomat before being elected to Parliament, he spent 11 years in opposition during the conservative coalition government of the Liberal and National parties. But under his leadership, Labor won a decisive electoral victory in November 2007.
Despite reaching record high levels in popularity polls, Rudd's approval -- with the public and with fellow Labor MPs -- had waned by 2010 and when he tried to impose additional taxes on Australia's powerful mining industry, Gillard -- his deputy at the time -- challenged him for the leadership and won. In the aftermath of Rudd's fall there were widespread reports that his leadership style -- said to have been secretive, interfering and erratic -- alienated a lot of Labor MPs and bureaucrats.
Gillard accused him Thursday of being "an excellent campaigner," but having "very chaotic work patterns" that resulted in "paralysis in the government."
Gillard called an election in late 2010, and a big drop in support for Labor resulted in a hung parliament. Eventually three independent MPs backed Gillard, enabling her to govern with a razor-thin majority. But she has never achieved Rudd's high levels of popularity and the prospect of Rudd challenging her for the prime ministership has been swirling and swelling, very publicly, for months.
CNN's John Raedler contributed to this report