Andy Burnham has warned there is a "real risk" Labour could split if he does not defeat left-winger Jeremy Corbyn for the leadership.
The shadow health secretary said the party was at a "fork in the road" and could end up divided and irrelevant.
The comments, in an interview with the Sunday Mirror, underline the growing fear among Labour big hitters that Mr Corbyn could pull off a shock victory.
Blairite Liz Kendall and shadow home secretary Yvette Cooper have been coming under pressure to pull out to try and consolidate the centrist vote.
Writing for the newspaper, ex-Cabinet minister David Blunkett branded the 66-year-old Islington North MP representative of "the Old Left" and lacking answers to today's problems.
"These spasms of self-indulgence are not new ... But now is the time for them to stop," he insisted.
Mr Blunkett said he would be backing Mr Burnham for the leadership.
Mr Burnham said: "Labour is at a fork in the road. I am now worried that, if we take the wrong turn, there's a real risk that the party could split ...
"People who are being hit hard by this Tory Government urgently need Labour to come together and get its act together.
"Becoming a party of protest riven by factions is of no use to them whatsoever. If that is what happens, they will conclude Labour has become irrelevant and they would be right.
"Labour must use this leadership election to call time on factionalism and division."