Voters had given Labour a "big thumbs down", Paul Kenny said
The general secretary of one of Britain's biggest trade unions has called for Gordon Brown to face a leadership challenge this autumn.
The GMB's Paul Kenny said MPs should make a "strong decision" ahead of the next general election.
But Tony Woodley, joint leader of the Unite union, said a changing leader was "not the solution" to Labour's woes.
Their remarks follow the party's defeat by the SNP in Glasgow East and as leading figures meet to discuss policy.
The three-day Labour National Policy Forum will consider new ideas and amendments to the current programme.
It brings together 55 constituency parties and 30 trade unions, as well as other socialist movements.
The unions, which now account for the vast majority of Labour funding, are reportedly putting about 100 demands on issues ranging from new rights for workers to free school meals for all primary school pupils.
Mr Kenny told the BBC that Labour MPs should hold a leadership contest this autumn to clear up questions surrounding Mr Brown's future.
On the by-election, which saw the SNP overturn a Labour majority of 13,507 to win by 365 votes, he said: "There's no point dressing it up. It was an unmitigated disaster."
Mr Kenny added: "The reality is people gave a big thumbs down to the Labour Party. If you don't accept that, you've got nowhere to go."
He added that he understood it was normal Labour Party procedure to send out leadership nomination papers to its MPs over the summer, even if there was no challenge.
Mr Kenny also said that if 20% nominated a rival contender, then there had to be a contest.
He said it was "better to have the ballot" and "see where we go".
"The MPs have got to make a strong decision as to whether they want to go into an election with Gordon Brown or have a [leadership] contest."
But his call was rebuffed by Mr Woodley, who said: "The result in Glasgow was clearly disappointing. One thing we do know, however, is that changing the prime minister isn't the solution.
"The change people want - in Glasgow and around the country - is a change of political approach. Blairism should finally be buried in Glasgow's East End.
"For too long the government has put all its eggs in the free-market basket. People are now looking for more support and protection from government as we face serious economic difficulties rooted in City excesses."
Mr Brown was chosen as Labour leader last year, after his only rival - leftwinger John McDonnell - failed to amass enough support among fellow MPs to go to a ballot of party members and unions.