Unions have raised fears of job losses at defence giant BAE Systems if the Government pulls back from orders to build frigates.
The GMB said unions had been warned of a "worst case scenario" of 800 job cuts, which would hit yards in Scotland.
The union is seeking talks with the Government over the future of the Scotstoun and Govan yards.
Gary Smith, GMB Scotland secretary, said: "This would be a total betrayal of the upper Clyde workforce by a desperate Tory government trying to shift the goal posts in the face of their failing economic stewardship.
"We've gone from the upper Clyde workforce being promised the manufacture of 13 Type-26 frigates in 2014, for that to be cut to eight frigates last year.
"We've gone from promised investment that would secure thousands of skilled jobs and hundreds of apprenticeships for a generation, only to be told to prepare for redundancies.
"In the same week that Scottish unemployment increased by 20,000, the prospect of significant job losses at Govan and Scotstoun doesn't even bear thinking about - it could tip our economy over the edge.
"GMB Scotland rejects this typically ruinous Tory agenda and we will resist any redundancies or withdrawal of work on the upper Clyde by using every tool we have at our disposal."
A BAE Systems spokesman said: "Following the Strategic Defence and Security Review, we are working with the Ministry of Defence to agree a revised baseline for the Type 26 ships and a production schedule for the two additional Offshore Patrol Vessels in Glasgow.
"We are engaging our trades unions as we work through this process. Our focus is to deliver the capability the Royal Navy needs, while ensuring the best value for UK taxpayers."
Unite Scottish secretary Pat Rafferty said: "The Clyde has a proud tradition of shipbuilding and is home to some of the best shipbuilders making some of the best ships in the world.
"Those shipbuilders received a promise before the Scottish referendum from the UK government that their future would be secure. A failure by Defence Secretary Michael Fallon to honour that promise and fulfil the promised Type 26 frigate programme would be an act of betrayal, leaving shipbuilding on the Clyde hanging by a thread."
National officer Ian Waddell added: "We will be seeking an urgent meeting with Michael Fallon to demand assurances that he honours his government's promises as well as pressing BAE Systems to hold its nerve and keep faith with its workforce.
"Britain has a proud tradition of shipbuilding which could be holed beneath the water if these reports are true and significantly diminish our sovereign defence capability.
"Rather than leading defence workers up the garden path, the Government needs to support them by giving them assurances that it will fulfil its commitment on the Type 26 frigate programme."
Nicola Sturgeon said Clyde workers had been given "very clear commitments" that they would have the contracts to build the Type 26s and that their jobs would be safe.
The First Minister said: "We have already seen the UK Government cut back on the size of the order. Reports that the vessels may not be built in Glasgow at all are deeply troubling.
"It would be unacceptable for the UK Government to renege on its commitment to build these ships on the Clyde. The workforce at BAE in Glasgow is second to none and the promises made to them must be honoured.
"We will be pursuing these reports thoroughly and offering all our support to the workforce and to BAE systems to ensure that the contracts are delivered in full on the Clyde."
Scottish Labour leader Kezia Dugdale said: "If these reports are correct, workers on the Clyde will have been betrayed by a Tory government making false promises.
"Shipyard unions will have the full support of Scottish Labour in protecting these jobs. Clydeside shipbuilders are the best in the world and investment in the yards so that facilities match the skills of the workforce is essential to allow them to win future contracts.
"It is essential that the Type 26 project goes ahead as planned and as promised."
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