Unions at BAE Systems have warned of possible delays to funding for the Royal Navy's new frigates.
But Scottish Conservative leader Ruth Davidson insisted there was no change to the timetable.
Labour said it was vital that promises were kept while the Lib Dems called for an end to uncertainty.
The UK government confirmed in its Strategic Defence and Security Review last November that eight Type 26 frigates would be built on the Clyde, although the total number was scaled back from 13.
In the meantime, the yards are being sustained by Ministry of Defence orders for new offshore patrol vessels.
But after briefings with management, the GMB union said last week that work on the new frigates would not begin until 2017 and raised concerns that up to 800 jobs could be lost if there was any backsliding on commitments.
SNP leader and Scottish First Minister Nicola Sturgeon said she was "gravely concerned" by the developments.
She said: "The future of both Govan and Scotstoun depend on these orders. Solemn promises were made in the run-up to the referendum and if those promises are broken, it will be seriously damaging for the shipyards but I think people across Scotland will feel very let down by the parties that made those promises."
She added: "I think the government has the responsibility to make cast iron assurances here."
Scottish Labour leader Kezia Dugdale said she had held discussions with shipyard workers and BAE management  about the need to protect jobs.
She said: "It's my deep regret that Labour didn't win the general election - so the Tories have to fulfil their promise to the workers in the yards, and I'll be making that case every step of the way."
Scottish Liberal Democrat leader Willie Rennie also expressed frustration about the uncertainty.
"There are serious concerns about the future of orders at the yards and it's important that the Conservative government gives an absolute commitment. We've got to end this feast and famine of orders at the yards," he said.
The Scottish Conservative leader Ruth Davidson, however, said she had been given assurances by Defence Secretary Michael Fallon that nothing had changed.
She said: "He confirmed there had been no change to the orders that were set out in the Strategic Defence and Security Review last year.
"That means all eight Type 26 anti-submarine frigates that are coming, plus the light frigate order on top of that, and the two offshore patrol vessels. They are coming to the Clyde, as discussed last year, to the same timetable and the same number."
A spokesperson for BAE Systems 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."
First Minister Nicola Sturgeon has called for "cast iron assurances" jobs will not be lost at Clyde shipyards because of contract delays.