Union leader Paul Howes says he won't stand for a possible Senate vacancy in NSW, saying he did not want to divide the party.
"I do not want to be the type of person in this movement who destructs, who divides because of my own personal ambition," he told reporters in Sydney.
"Therefore I think it's in the interest of the movement that someone else takes that spot when it comes up."
There is speculation that former foreign minister Bob Carr will quit the Senate, creating the vacancy.
As an ALP Right faction powerbroker, Mr Howes played a role in Julia Gillard's overthrow of Kevin Rudd as prime minister in 2010.
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He also plays an active role on the ALP's national executive and faction-riven NSW branch.
He believed he would have had majority support in the party to run for the Senate vacancy, but it would have been a "pretty ugly and messy fight".
"Ultimately I made this decision because I don't want to be a wrecker and I don't want to divide," Mr Howes said on Thursday.
"I don't want to have the branch of the party here in NSW and our movement rip itself apart over me personally.
"When you've gone through what we've been through in the last six years you recognise how destructive, how damaging, how distracting this type of politics is."
Senator Carr's senior adviser Graeme Wedderburn has told The Australian newspaper he would like to be considered to fill the vacancy.
"I've got Bob's support, but he appreciates how complex these matters are," Mr Wedderburn said.
NSW Labor secretary Jamie Clements, who also hails from the Right faction, is understood to be backing former federal MP Deborah O'Neill.
Another possible candidate is NSW ALP vice-president and member of the ALP national executive, Tara Moriarty.
Prime Minister Tony Abbott said Labor needed to learn that voters did not want "faceless men" running the Labor party or taking up positions in parliament.
"It seems to me the Labor party is very much in denial about the fact they have just had a thumping defeat," Mr Abbott told reporters in Sydney.
