Jim Murphy is facing growing calls to step down as Scottish Labour leader from critics inside the party after overseeing its worst electoral defeat in its history.

A group of centre-left MSPs, trade unions including Unite and former MPs who lost their seats in last week’s rout is openly challenging Murphy’s leadership before a Scottish Labour executive meeting on Saturday.

Scotland’s largest union Unison gave Murphy breathing space after it stepped back from calling for his resignation but it said on Tuesday that it could support calls for him to stand down if “a wider movement proposed change”.

“It is unprecedented for a party leader not to stand down after such a defeat, particularly when he loses his own seat,” Unison’s Labour affiliation committee said. “The [Scottish Labour] 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.”

That split in the party will deepen later on Wednesday when some of Murphy’s leading critics meet in Glasgow at a meeting organised by the Campaign for Socialism, which is closely aligned with Murphy’s main challenger for party leader last year, Neil Findlay MSP.

It is widely expected that Murphy, Scottish Labour’s fifth leader in seven years, will secure the executive’s support this weekend after a majority of Labour MSPs and its sole surviving MP, shadow Scottish secretary Ian Murray, backed his decision to remain in his post.

But organisers of Wednesday’s anti-Murphy meeting are canvassing support from constituency Labour parties in a bid to push Murphy into voluntarily standing down, and to coax other critics of his leadership at Holyrood into publicly calling for his resignation.

Stephen Low, a Unison official and an organiser of the Campaign for Socialism meeting, said Murphy’s position was made impossible because last week’s election defeat, where Scottish Labour lost 40 of its 41 seats and lost roughly 400,000 votes, proved that he was a clear electoral liability.

He said Murphy’s credibility would be open to constant challenge because he no longer had a parliamentary seat. Failing to replace him before next year’s Holyrood parliament elections greatly increased Labour’s chances of another catastrophic defeat to the SNP.

“It’s not just the fact he has lost his seat; it is not just the fact he was the guy on deck when [the defeat] happened. He was in complete control of the election campaign and the campaign was a shambles,” Low said.

He said Murphy’s campaign lurched from trying to woo back Labour voters who voted yes to independence, to then attacking the independence cause in an effort to appeal to Tory and Lib Dem tactical voters. “If you talk to anybody who is not in the Labour party, they’re actually bewildered that he’s still in place,” Low added.

In a series of blows to Murphy this week, Alex Rowley, the MSP and former Fife council leader who was a close ally of Gordon Brown’s, has resigned his frontbench post, with three other MSPs publicly questioning Murphy’s continued role as leader.

Four MSPs have now openly criticised Murphy’s decision to remain in post. After Unite and the rail union Aslef – both known opponents of Murphy’s original leadership bid – called for him to step down, the GMB engineering union backed him.

Murray, the Labour MP for Edinburgh South, said he supported Murphy’s continuing leadership despite the scale of the party’s defeat last week. Murphy and his deputy Kezia Dugdale had only been in post for five months and needed more time to rescue the party.

“The outcome was at the top end of our worst nightmares but the general trend had set in some time before the election,” he said. “We need time to reflect and we need time to put together a programme for change. We’re not going to regain the trust of the Scottish people by finding TV cameras [to complain to], by finding very simple answers to incredibly difficult questions.

“There is no point to us rushing to conclusions. One or two people breaking off to demand his resignation isn’t helpful.”