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Mr Bowen, a member of the ALP right, formally announced his bid on Tuesday morning in front of the house where he grew up in Sydney's Smithfield.
"I think the party does deserve contest. I think that the party deserves a choice," he told reporters.
He took ownership of Labor's franking credits policy which was devastatingly described as a "retiree tax" by the coalition during the campaign, but said the party would start with a blank policy slate for the coming term.
"No political party ever takes to the next election, exactly the same policies they took to the last. That would be dumb."
Mr Albanese, from the party's left, indicated on Sunday he'd make a second tilt for the leadership, which he lost to Bill Shorten in 2013.
He's been campaigning strongly since, saying Labor needs to take a hard look at some of its policies.
"We got one-in-three Australians to vote for us. That's the truth. That is not good enough," he told 3AW radio.
He said many voters had contacted him about the franking credit overhaul.
"In many cases people who were getting a relatively small amount ... but it was that two or three thousand dollars that they were using to pay their rates, to pay their car rego, for a holiday at the end of the year," he said.
It could be capped or grandfathered, he said.
Nevertheless, he thought the Morrison government would have to act on the issue because its near $A8 billion ($NZ8.4 billion) a year cost to the budget was unsustainable.
Deputy leader Tanya Plibersek, also from the left faction, ruled herself out on Monday, saying it was not her time.
Mr Bowen said if she wanted to stay on as deputy and the caucus agreed, he would be happy to work with her.
Other potential deputies he floated were Linda Burney and Mark Butler, although he won't be running on a ticket with anyone.
The leadership will be decided by a vote of grassroots members and the federal parliamentary caucus, with each group given 50% weight.
Caucus will not be told the result of the grassroots vote before MPs make their decision.
Mr Albanese won the grassroots vote in 2013 but did not get enough caucus votes to defeat Bill Shorten.
"I'm happy to concede that Albo probably goes in favourite,' Mr Bowen said.
"The Labor Party went in on Saturday as favourite, too. I'm a bit over favourites."
Mr Shorten will continue as Labor's interim leader until the party's leadership is determined.
The party's national executive will meet on Wednesday to formalise nominees and start the ballot process.