Andy Burnham has warned Labour activists that electing Jeremy Corbyn as leader would mean "giving up" on winning the next election.
The shadow health secretary's intervention came with the left-winger embroiled in yet another row over past comments - this time for suggesting it was a "tragedy" Osama bin Laden was killed by the United States.
The leadership frontrunner made the remarks shortly after the 2012 special forces raid on the al Qaida chief's Pakistan compound in which he and four others were shot dead.
In a clip from the Iranian Press TV show The Agenda, Mr Corbyn is heard complaining that there had been "no attempt whatsoever that I can see to arrest him and put him on trial, to go through that process". He went on: "This was an assassination attempt, and is yet another tragedy, upon a tragedy, upon a tragedy.
"The World Trade Centre was a tragedy, the attack on Afghanistan was a tragedy, the war in Iraq was a tragedy. Tens of thousands of people have died. Torture has come back on to the world stage, been canonised virtually into law by Guantanamo and Bagram.
"Can't we learn some lessons from this? Are we just going to sink deeper and deeper?"
A spokesman for Mr Corbyn said he was "a total opponent of al Qaida, all it stands for".
But Liberal Democrat leader Tim Farron said Mr Corbyn was "utterly wrong".
"Bin Laden's death was not a tragedy. The tragedy was the 2,977 who died during that awful day. We remember them," he said.
George Osborne has also waded into the Labour contest by claiming a party led by Mr Corbyn would pose a threat to national security by threatening the future of the UK's nuclear deterrent.
The Chancellor said "an unholy alliance of Labour's left-wing insurgents and the Scottish nationalists" would shatter decades of near-unbroken Westminster consensus in favour of maintaining a capability.
Both Mr Corbyn and the SNP are opposed to the renewal of the Trident missile system being pursued by the Conservative Government.
In his article this evening, Mr Burnham dismissed the challenges from fellow candidates Yvette Cooper and Liz Kendall.
And he attempted to win over activists attracted to Mr Corbyn's radical agenda by insisting there would still be "big change" if he won.
"I believe I'm the only candidate offering big changes, but who can also get our party back into power in 2020," he said.
"So I want to make a direct appeal to those members and supporters who are thinking of voting for Jeremy, or who are still undecided.
"I know you are unhappy with politics as usual and you have a desperate desire for big changes. I understand that and share that desire for change ...
"Under my leadership, we will fight the next election on a radical manifesto, with bold ideas such as integrating the NHS and social care and renationalising the railways."
He added: "As the leadership contest draws to a close, but with thousands of people still undecided on how to vote, I say very clearly: Don't give up on wanting to see big changes, but don't give up on winning either."