Prime Minister David Cameron’s official spokeswoman said it was “reasonable” for General Sir Nicholas Houghton, as the Government’s senior military adviser, to speak publicly on the issue.
Mr Corbyn has written to Defence Secretary Michael Fallon asking him to rein in the Chief of Defence Staff. The Labour leader regards the comment as an unacceptable breach of the principle that the military do not interfere in politics.
But Mr Cameron’s spokeswoman said: “The chief of the armed forces... made a point about the credibility of the deterrent. He made clear he wasn’t talking about a personal thing.
“He was asked about the deterrent. He made a point about the credibility of the deterrent. And as the principle military adviser to the Government, it’s reasonable for the Chief of Defence Staff to talk about how we maintain the credibility of one of the most important tools in our armoury.”
The row erupted on Remembrance Sunday just hours after Mr Corbyn and Gen Houghton laid wreathes in memory of Britain’s war dead at the Cenotaph in Whitehall.
In a BBC interview, Gen Houghton expressed concern that Mr Corbyn had declared there were no circumstances in which he would press the nuclear button should he become prime minister.
“It would worry me if that thought was translated into power,” he told The Andrew Marr Show.
“The reason I say this - and it’s not based on a personal thing at all - is purely based upon the credibility of deterrence. The whole thing of deterrence rests upon the credibility of its use.
“When people say they’re never going to use the deterrent, I say you use the deterrent every second of every minute of every day - the purpose of the deterrent is you don’t have to use it because you effectively deter.”
In a strongly-worded statement, Mr Corbyn said it was a “matter of serious concern” that the Chief of the Defence Staff had intervened directly in “issues of political dispute”.
“It is essential in a democracy that the military remains political neutral at all times,” he said.
“By publicly taking sides in current political arguments, Sir Nicholas Houghton has clearly breached that constitutional principle.”
Former First Sea Lord, Admiral Lord West, said the general had said “a little bit more than he should have done”, but insisted the row had been “overblown”.
“We (military figures) tend to say things as we see things rather than spinning them or being clever with our words,” the Labour peer and former security minister told BBC Radio 4’s Today programme.
“He was trying to be careful but he got bluffed into saying a little bit more than he should have done.”
The peer said no action was needed against Sir Nicholas other than to advise him to “be careful”.
Lord West also indicated that he was likely to resign the Labour whip if the party opposed the renewal of the Trident system - although he suggested Mr Corbyn “may well change his view”.
“I think it is highly likely I would resign the whip,” he said.
Labour’s shadow defence secretary Maria Eagle said she saw nothing wrong with Gen Houghton’s comments and echoed his concerns about Mr Corbyn’s position on Trident.
But there was backing for the Labour leader from the Conservative chairman of the Commons Foreign Affairs Committee, Crispin Blunt, who said the general’s comments had overstepped the mark.
“As an ex-soldier and a Conservative politician I am rather loath to take the side of a left-wing leader of the Labour Party against the Chief of the Defence Staff, but I rather fear he has a point,” he told Sky News.
“I think the Chief of the Defence Staff perhaps strayed into political territory.”