A senior Labour MSP says the party is heading for "disappearance" in Scotland unless Jim Murphy resigns as leader.
Alex Rowley, the MSP for Cowdenbeath, has quit his role as Labour's local government spokesman at Holyrood and urged Mr Murphy to stand down.
Another Labour MSP, Elaine Smith, has backed Mr Rowley's call saying the party needs "new direction."
Scotland's only Labour MP Ian Murray accused those criticising Mr Murphy of "digging knives into the party".
Pressure has been growing on the Scottish Labour leader to step down following last week's general election results.
Labour lost all but one of its 40 Scottish seats to the SNP in last Thursday's election. Mr Murphy's once-safe majority in East Renfrewshire - a seat he had held for nearly 20 years - was eliminated by the SNP's Kirsten Oswald.
Unison Scotland has also called for a "radical change in approach" from the Labour party in Scotland.
The union said it was not its place "to initiate a change in leadership" but said if there was a wider movement proposing change it would "not oppose it".
It comes after both the Unite union and the train drivers' union, Aslef, called on Mr Murphy to resign.
By Brian Taylor, BBC Scotland political editor
Alex Rowley is a Holyrood new boy, entering parliament via a by-election in January last year. But he is very far from a beginner in Labour politics. He has been at various times a council leader, the party's general secretary in Scotland and a senior aide to Gordon Brown.
So, when he says that Jim Murphy should quit as Scottish Labour leader, he commands a degree of attention.
Only a degree, mind. Among Labour at Holyrood, there are as many views about the future of the party as there are group members. By contrast, the Scottish Labour group at Westminster is entirely united.
Mr Rowley is adamant that he is not revisiting the leadership contest which followed the departure of Johann Lamont. (He backed Neil Findlay.) And he praises Mr Murphy's energy and application.
Mr Rowley is a former general secretary of the Labour Party in Scotland and ran Neil Findlay's campaign for the leadership against Mr Murphy last year.
Before being elected as an MSP, Mr Rowley was a councillor in Fife and worked as an assistant, election agent and constituency manager to Gordon Brown. He is considered by some as Mr Brown's "right-hand man and protégé".
Mr Rowley said Labour needs "a fundamental change in direction and strategy" but he told the BBC Mr Murphy and his aides had focused instead on loyalty to the leadership.
He warned that if Mr Murphy remained leader, Labour was heading for another big defeat at the Holyrood elections in 2016.
The MSP's resignation letter said he thought Mr Murphy's post-election result speech, in which he vowed to stay on as leader, was "a mistake".
Mr Rowley wrote: "I sincerely hold the view that you continuing as leader whilst not in the Scottish Parliament, and not in an elected position holding a democratic mandate, means you will become an unhelpful distraction from the real issues that Scottish Labour must focus on."
Mr Murphy met Labour MSPs on Monday to discuss the party's disastrous election performance.
Mr Rowley added: "It is clear from the discussion yesterday that dissent in public from the leadership view is perceived as disloyalty, but I am convinced we need a fundamental change in direction and strategy and therefore cannot sign up to your leadership as one of your shadow team."
A spokesman for the Scottish Labour Party said: "It's disappointing that Alex chose to resign. The task for the Scottish Labour Party going forward is to work together to rebuild our movement and regain the trust of the people of Scotland."
'Knee jerk reactions'
Elaine Smith, Labour MSP for Coatbridge and Chryston, praised her colleagues, Mr Rowley and Mr Findlay, for resigning as party spokesmen.
She said: "They are putting loyalty to the Labour Party ahead of personal career or position and I think Jim Murphy should do likewise and step down as leader.
"In the face of the worst result for Labour since 1918 we do need a new direction."
She is a member of the Campaign for Socialism which has already called on Mr Murphy to "stand aside".
Scotland's only Labour MP, Mr Murray, hit out at those calling for Mr Murphy to stand down immediately.
The shadow Scottish secretary said the last thing any party should do after a heavy election defeat is make "knee jerk reactions and turn in on themselves".
He said: "Everyone who is looking for a camera and a TV studio to dig knives into the Scottish Labour party should go home, sit in a darkened room, reflect how the election was lost and work together."
A statement from Unison Scotland's Labour Link said: "It is unprecedented for a party leader not to stand down after such a defeat, particularly when he loses his own seat.
"The campaign may have been energetic, but it lacked focus and clearly voters do not regard Jim Murphy as a credible messenger of Scottish Labour values.
"Scottish Labour has a limited period of time to reorganise itself to provide a credible challenge in the Scottish Parliament elections next year."
At the weekend, the Unite union said the Labour leader should go "without delay" and warned that, otherwise, "extinction looms" for the party.
After Monday's three-hour meeting of Labour MSPs, finance spokeswoman Jackie Baillie told the BBC that the "overwhelming majority of MSPs were very clear, they want Jim Murphy and Kezia Dugdale to lead us forward into the future".