An article published in The Times on Saturday quoted two ‘senior civil servants’, with one suggesting there are concerns in Whitehall that Mr Corbyn is ‘too frail and is losing his memory’.
Mr Corbyn, 70, called the report a ‘farrago of nonsense’ and described himself as a ‘very fit, very healthy, very active person’.
The Labour leader added: ‘The idea that civil servants should be briefing a newspaper against an elected politician, against a prospective government, is something that should be very concerning to a lot of people.
‘The civil service has to be independent.
It has to be non-political and has to be non-judgmental of the politicians they have a duty to serve.
‘There must be an investigation into which senior civil servants are spreading fictitious information to the press and in the process compromising the integrity of the civil service.’
The Times’ front page story claimed there are fears Mr Corbyn is being ‘propped up’ by his advisers.
One source was quoted as saying: ‘There is a real worry that the Labour leader isn’t up to the job physically or mentally but is being propped up by those around him.
‘There’s growing concern that he’s too frail and is losing his memory. He’s not in charge of his own party.’
Labour strenuously denies the claims, saying suggestions that Mr Corbyn does not make his own decisions are ‘laughable’ and ‘demonstrably false’.
A spokesman said: ‘Jeremy Corbyn leads an active life, running and cycling regularly, and is in good health.
‘Reports to the contrary are scurrilous and a transparent attempt to undermine Labour’s efforts to redistribute wealth and power from the few to the many.’
Mr Corbyn also received backing in the matter from former Ukip MP Douglas Carswell.
He tweeted: ‘I’d rather have my country run by democratically elected Jeremy Corbyn than the smug, self regarding, incompetent Whitehall officials that briefed this to the Times.’
When asked about reports Corbyn was mentally and physically unfit for office Unite leader Len McCluskey attacked journalists for ‘fake news’.
‘They ought to be ashamed of themselves,’ he said. ‘It was fake news, it was lies, it was distortion.
‘Jeremy Corbyn is fit as a fiddle, he is one of the strongest people I have ever met – people 20 years younger struggle to keep up with him.
‘I don’t believe them at all – it’s the Murdoch press, of course they are going to attack and try to undermine Jeremy.’