Nicola Sturgeon claimed “only the fullest possible assurance” from the UK Government would be acceptable in response to claims made by a whistleblower which came to light at the weekend.
Able Seaman William McNeilly, 25, went absent without leave last week after producing an 18-page report containing a series of allegations about the Trident submarines based at Faslane on the Clyde.
He was stopped at Edinburgh Airport on Monday and is being held by Royal Navy Police at a military establishment in Scotland.
The Royal Navy said it is “continuing to investigate the circumstances”.
Speaking at First Minister’s Questions, Ms Sturgeon said: “Recent allegations from a whistleblower highlighting a catalogue of safety breaches and security lapses are gravely concerning.
“The UK Government must fully investigate these allegations without delay, explain any failings that have been highlighted and set out as far as they can what is being done to address each one.
“People across Scotland, and indeed the UK, not least those who live and work around the naval base on the Clyde, must have answers to the very serious allegations that have been raised.”
She added: “Public safety must always be the top priority. I do think we need a top-level inquiry into the allegations that have been made.
“Any potential safety or security failings of the Trident nuclear weapons system are an extremely grave matter.
“The government has long opposed the existence of these weapons but we have also raised operational and safety concerns in the past as well.
“Allegations that were raised over the last few days are all the more troubling because they were raised by a member of defence personnel, and therefore they have got to be treated with the seriousness they deserve.
“I think only the fullest possible assurance from the UK Government of the safety of its arrangements is acceptable.”
A Royal Navy spokeswoman said: “The Royal Navy would like to reiterate that we take the operation of our submarines and the safety of our personnel extremely seriously.
“We continue to fully investigate the circumstances of this issue and ministers will update Parliament at the earliest opportunity.”