Andy Burnham is the preferred Labour leader among people who voted for the party in the general election, as well as the favourite of the general population, according to a new poll.
The survey by market research company Research Now came amid indications that Mr Burnham is trailing behind far-left contender Jeremy Corbyn among those who actually have a vote in the ballot to choose a successor to Ed Miliband.
Labour former Cabinet minister Jack Straw has warned the party faces "oblivion" if it adopts the leftist policies of Mr Corbyn, who has picked up support from major unions including Unite and Unison and was expected to lead in constituency nominations when they close at midnight.
But Mark Serwotka of the PCS union said he believed the veteran Islington North MP would do "so much better" in the next election than Mr Miliband managed in May because he offered "hope of a different way".
In the Research Now poll of 1,001 members of the public, regardless of political affiliation, Mr Burnham was picked as the best choice for Labour leader by 30% of those who expressed an opinion, ahead of 24% for Mr Corbyn and Yvette Cooper and 21% for Liz Kendall.
When the same question was put to those who backed Labour in May - many of whom will not be registered to vote in the leadership election - Mr Burnham extended his lead on 36% to Mr Corbyn's 28%, with Ms Cooper (20%) and Ms Kendall (16%) trailing. Among Liberal Democrat voters, Ms Cooper was the favourite, followed by Ms Kendall.
The Burnham camp said the survey indicated their candidate had the broad appeal needed to win over the voters which Labour needs to return to power in the election scheduled for 2020.
A campaign spokesman said: "Andy is the clearly the candidate to win back lost voters to Labour and unite the party at the same time."
The findings came amid growing signs of rancour in a campaign which still has six weeks to run, with postal ballot papers not even being sent out until August 14.
Dave Ward, deputy general secretary of the Communication Workers' Union (CWU), came under fire from Ms Kendall for describing followers of former prime minister Tony Blair as a "virus" in the party to which Mr Corbyn was the antidote.
Describing his words as offensive, Ms Kendall, who is viewed as the Blairite candidate, said: "Actually what we need is an antidote to the Tories."
But Mr Ward stood by his comment, telling BBC Radio 4's Today: "I want to see a party that stands up for workers again, that stands up for the disadvantaged in society, and puts those principles first without compromising those principles just in pursuit of an election victory."
Mr Straw said New Labour was a "very strange virus" which had delivered three election victories from which unions and their members benefited.
"The choice for people like Mr Ward is whether they retreat into a comfort zone of far-left policies which will lead to oblivion for the Labour Party or whether we accept the world as it is with a market economy but seek through Labour's values to moderate how that market economy works for the benefit of everyone," said the former foreign secretary. "That 's what New Labour was about and it worked brilliantly."
Sir Ken Jackson, former general secretary of the Amicus union, said: "There were things I could disagree with the Blairite government, but at the end of the day you have to achieve power, you have got to persuade people.
"I don't know what Labour can do for working people when they are in permanent opposition."
Research Now questioned 1,001 people online on July 28 and 29.