John Ainslie said he was "concerned" by the "dangerous situation" following a Royal Navy submariner claiming the country's Trident programme is a disaster waiting to happen.
Seaman William McNeilly has now gone missing after posting pictures online highlighting a series of safety and security lapses.
He's since said he will hand himself into police for breaking the law by publishing his document claiming the UK's weapons were open to being "infiltrated by a terrorist".
He wrote: "Our nuclear weapons are a target that's wide open to attack.
"It is just a matter of time before we're infiltrated by a psychopath or terrorist."
John Ainslie from the CND said Mr McNeilly must be taken seriously: "He's done his training and looked at the manuals and then when he's actually going out to sea on patrol he's finding a list of things going on which are not in line with what should be happening.
"Some are things that he's actually seeing himself and some are reports that he's hearing second hand from others and in both cases I find them quite concerning, I mean, he describes a fire in the missile compartment."
The Royal Navy said it is ''concerned for Mr McNeilly's whereabouts and well-being'' adding that police were searching for him.
A spokeswoman said that his claims were ''subjective and unsubstantiated personal views, made by a very junior sailor, with which the naval service completely disagrees''.
She added: "'The Royal Navy takes security and nuclear safety extremely seriously, and we are fully investigating both the issue of the unauthorised release of this document and its contents.
''The naval service operates its submarine fleet under the most stringent safety regime and submarines do not go to sea unless they are completely safe to do so.''
The Prime Minister's official spokesman said: "As with all defence equipment, they only operate where we believe the right standards are in place."