A former Labour First Minister of Scotland has warned that voters see a "nasty" element within the party as he gave only partial support for Jim Murphy to remain in post.
The Scottish Labour leader is under intense pressure to resign in the wake of Labour's disastrous general election result north of the border.
Unions and former candidates have lined up to call on him to step aside, while one member of his shadow cabinet has resigned.
Reports suggest Mr Murphy could even face a motion of no confidence tabled at the party's Scottish Executive Committee (SEC).
Former First Lord McConnell called for a "proper debate" within Labour on Mr Murphy's vision for the party.
He rejected "score settling" as he said: "I think one of the problems in the past is that we have been seen to have a kind of nasty element in the party and to be seen to be looking at each other all the time."
But, he added : "I would like to see (Mr Murphy) laying out exactly what he wants to do and I would like to see there being a proper debate inside the party about that."
"I would like him and Kez (Dugdale, his deputy) to get time to have that discussion and then I would also like him to engage with not just party members but voters and ex-voters and I think over that period of time it will become clear what should happen next."
Mr Murphy has insisted that he is staying, despite the party winning just one of the 41 Westminster seats in Scotland it took in 2010.
Asked if the current leadership team should stay until after next year's Scottish Parliament election, he said: "They should certainly stay for the moment, and we should have a proper discussion inside the party about the way ahead."
Lord McConnell also said he believed the "rot" in the Scottish Labour Party had "started further back than eight years ago".
"I think we've had a problem as a political party particularly amongst our Westminster representatives in responding in the post devolution era," he said.
He called the Smith Commission proposals for extra devolution to Holyrood a "shambles" and called instead for a UK-wide constitutional convention.
One Labour MSP, Neil Findlay, who stood against Murphy for the leadership, has already resigned from the Scottish shadow cabinet, although he ruled out a leadership challenge.
The Unite and Aslef unions also urged Mr Murphy to stand aside.
Unite's Scottish leader Pat Rafferty said: "Either Scottish Labour rediscovers its mission as the natural voice for social justice in our nation, or irrelevance and ultimately extinction looms."
Former Scottish health minister Andy Kerr accused Mr Murphy of being part of the problem.
"My worry is that Jim's a product of the system who saw Scotland through the prism of their deep hatred for the SNP; they forgot to see Scotland through the prism of the Scottish people and how they are changing."
He also compared the campaign to "dad-dancing in the most modern nightclub in the city of Glasgow".
Former MP Katy Clark, who lost her seat on Thursday night, called on him to reconsider his position.
Michael Connarty, another ex-MP who also lost his seat, said he thought Mr Murphy "should go".
But others within Labour turned their ire on Ed Miliband, saying that the Westminster leader crippled them when voters went to the polling booths.
One former candidate blamed Ed Miliband. "What we really needed in many seats was Tories and Lib Dems to back us. And it was very clear that Ed was hurting us on that issue," he said.
"They just could not bring themselves to back Ed".
Others, including some on the left of the party, are understood to be keen that Mr Murphy remains in place, fearing another change of leadership could damage the party's chances in next year's Holyrood elections.
Gordon Matheson, the leader of Glasgow City council, said the party wold have lost even if Jimmy Maxton or Keir Hardie had been in charge.
Others offered alternative to solutions to Labour's woes.
Ex-First Minister Henry McLeisjh called on the party to cut its ties with the rest of Labour and become an independent party.
That idea was rejected by Scottish Labour's only remaining MP Ian Murray.
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