Tanya Plibersek has announced she will not contest the Labor leadership.
Ms Plibersek said she’d received support across the party to be elected leader, after Bill Shorten resigned on election night.
“But now is not my time,” she said in a statement on Monday.
“At this point, I cannot reconcile the important responsibilities I have to my family with the additional responsibilities of the Labor leadership.”
Ms Plibersek intends to continue as Labor deputy leader, until the party’s leadership is determined.
“At that point, I will serve in whatever capacity my colleagues best think can help Labor return to government,” she said.
Mr Shorten was supporting Ms Plibersek for the leadership, and would likely have brought the Victorian right with him.
Julia Gillard had also backed Ms Plibersek, in a rare intervention into party politics from the former prime minister.
Her left factional colleague Anthony Albanese is the only person to publicly enter the Labor leadership contest so far.
Shadow treasurer Chris Bowen, from the Labor right, is still considering whether he will run.
Labor’s national executive committee met on Monday to lay out the framework for the leadership ballot.
The full Labor executive, comprising senior MPs and key party officials, will meet on Wednesday.
The search for the next leader is expected to take about one month.
Rank and file members will first cast their votes, followed by the federal Labor caucus, before the results are averaged out and a winner is crowned.
Mr Albanese, who came second in the last leadership ballot in 2013, believes Labor needs to listen to people in the outer suburbs and the regions to understand why the party lost the election.
“What we need to do is never forget the economy is central and jobs are central and we need to talk to people about what their issues are, and what our plan for jobs is,” he told Adelaide’s 5AA Radio.
Opposition frontbencher Joel Fitzgibbon believes the party has drifted too far to the left.
“We certainly have to get back to the centre and we have to reconnect to our working class base,” he told ABC Radio National.
“Someone needs to indicate that they are the person who is prepared to put us back on track. And if someone’s not prepared to do that, well, I might just do it myself.”
Doug Cameron, a leading figure in the Labor left who retired from the Senate at the election, disagrees.
“This is not the time to panic and move to the ‘centre’ as a proxy for abandoning progressive policies and capitulating once again to neoliberalism,” he tweeted.
“There was no Morrison miracle, only a scare campaign prosecuted by the billionaires who control the media and the mining industries.”
Mr Fitzgibbon suffered a big swing against him in the NSW mining seat of Hunter, with voters favouring One Nation’s pro-coal candidate.
He said the opposition had equivocated over the Adani coal mine in Queensland.
“Chifley’s ‘light on the hill’ became a flickering light on Adani for the Labor Party.”