The SNP leader was reacting to suggestions from trade unions that up to 800 jobs could go from the Scotstoun and Govan shipyards if there are any delays to the contract to build Royal Navy warships in Scotland.
Unions voiced their concerns following a briefing last week from BAE Systems, the company contracted by the MoD to deliver eight Type 26 frigates.
Sturgeon said: “Workers at the Clyde yards were given a clear promise by the Tory Government and the Labour party that they would build the frigates and that their jobs would be protected. First the Tories cut the number of frigates, now we hear that they may delay or move the orders, putting jobs at risk. “The promises made to the workers at the Clyde yards must be met. David Cameron must commit to delivering these contracts, and ensuring jobs are protected at BAE on the Clyde.”
She added: “It would be an absolute betrayal if David Cameron was to go back on his promise now.”
The Scottish Conservative leader Ruth Davidson said she had sought assurances about the Clyde jobs from Defence Secretary Michael Fallon, who said the orders would go ahead. Davidson said: “It is important to monitor workforce issues at BAE between the winding down of work on the aircraft carriers and starting work on the Type 26 programme and I expect everyone – BAE, unions and government – to endeavour to make the transition between projects as smooth as possible and give the workforce the security they deserve.”