Alex Rowley’s criticism came as the company’s owners took the Scottish Government to task over criticism of its financial support.
Trades union leaders have also said the handling of the stricken yards - there are two in Fife and one on the Isle of Lewis - was “a growing scandal.”
The troubled engineering firm faces a bleak future after failing to land contracts for offshore wind farms.
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On Tuesday the Scottish Government said it could not give a £30m contract guarantee under existing state aid regulations, sparking a furious reaction from unions and politicians.
Today, BiFab’s Canadian owners, JVDriver, hit back, and said it had offered to transfer its shares to Scottish ministers at no cost - but got no response.
It said the offer remained open.
The growing political row engulfing BiFab continued with a strong attack from Mr Rowley, Labour MSP for mid-Scotland and Fife, and a former leader of Fife Council.
He said: “This statement from BiFab management makes it clear that the SNP and Tories have decided to allow BiFab to wither on the vine without exploring all options open to the company.
"It confirms that the SNP Government's pleas of 'no alternative' are simply weasel words from a party with no political will to secure skilled jobs in Scotland for the renewables sector.
“That the same SNP is this weekend speaking about a 'Just Transition' is a grotesque insult to the workers and communities in Fife and the Western Isles.
“This is an act of sabotage against Scotland’s manufacturing base that has already been decimated thanks to the SNP’s non-existent industrial strategy.”Mr Rowley called for UK and Scottish Parliament inquiries to “get to the bottom of why the Tories and SNP have made this unfathomable decision, and set out the alternatives that are clearly available."
Meanwhile, Neale Hanvey, SNP MP for Kirkcaldy and Cowdenbeath, has been in close contact with ministers to discuss BiFab this week.
On the contract guarantee, he said: “I share the serious concerns and frustrations that many will be feeling with this news and what it means for jobs in my constituency.
“Clearly the sands have shifted since my last meeting with the Scottish Government, so I have spent the day following up with ministers and other key figures across government and industry to seek the answers the community deserves.
“I have great confidence that Fife can play a vital role in the transition to a net-zero economy and I will continue to do everything I can to secure investment and deliver meaningful employment to my constituency. “
Gary Smith and Pat Rafferty, Scottish secretaries of the GMB and Unite unions, described the situation as “a growing scandal.”They added: “The signal this sends out to the renewables industry is clear, it’s business as usual. The jobs of the future will continue to be exported to the rest of world and subsidised by the billpayer to the tune of billions.
“At best, Britain will get scraps off the table from its own offshore wind market but it looks like both Governments have buried any credible hopes for a meaningful green jobs recovery in Scotland.”