It paved the way for a deal to install Mr Albanese unopposed, with finance spokesman Jim Chalmers as his deputy - though it is understood some in the party are still encouraging Mr Chalmers to run against Mr Albanese for the top job, and he is still considering that option.

Multiple Labor sources said a deal between Mr Albanese and Mr Chalmers was likely but not yet finalised on Wednesday afternoon.

Under that scenario, the ticket would call on Shoppies union figure Don Farrell to vacate the Senate deputy leadership position to allow a female duo of Penny Wong and Kristina Keneally to lead the Labor Party in the upper house.

At a press conference in Sydney, Mr Bowen said it was "clear" he would have been supported by a majority of Labor's parliamentary caucus, but Mr Albanese would command more support among the party's rank-and-file members "by a good margin".

He therefore decided to pull out of the race to avoid the need for a long and expensive ballot that he had no viable chance of winning, he said.

Mr Bowen used his speech to call on Labor's next leader to urgently fix what he viewed as the party's problem with religious voters.

"People of faith no longer feel that progressive politics cares about them. These are people with a social conscience who want to be included in the progressive movement," he said.

"We need to tackle this urgently. I think this is an issue from the federal election that we simply haven't yet focused on."

Labor figures from both the left and right factions who rushed to declare their support for Mr Albanese on Wednesday included Senator Wong, health spokeswoman Catherine King, Andrew Giles, Pat Conroy, Tony Burke, Senator Keneally and Terri Butler.

Senator Wong praised Mr Albanese as "the outstanding parliamentarian of our generation".

On Tuesday, Mr Bowen declared he was the best person to lead the economic agenda for a shattered Labor Party, despite his close connection as treasury spokesman to the economic policies that had just been rejected by the electorate at Saturday's election.

He said the party was "obviously not communicating with that part of society who would be natural Labor supporters", given they had not embraced the party's redistributive agenda.

Mr Albanese and Mr Bowen have both acknowledged a need to examine the party's policy offering following the shock defeat, and have spoken about reconnecting with regional and outer-suburban voters, who abandoned Labor in droves.

An uncontested appointment would allow Mr Albanese to immediately begin the process of reviewing Labor's campaign, which has also been widely criticised from within.

Common gripes included over-complicated and erratic messaging, failure to execute strong local campaigns in key seats and high levels of secrecy over polling data and other research.