A Whitehall investigation has been launched into claims civil servants branded Jeremy Corbyn “too frail” to be Prime Minister.
The Labour leader has said the reported comments raised concerns over civil service impartiality.
Theresa May ’s spokesman confirmed a probe was underway – and warned those responsible face disciplinary action.
He said: “We are taking the matter extremely seriously.
“The civil service is responsible for looking into any potential breaches of the civil service code, an this is no different.”
The comments were allegedly made at an event attended by senior civil servants.
The Times reported at the weekend that one senior civil servant said: “When does someone say [he] is too ill to carry on as leader of the Labour Party let alone Prime Minister?
“There must be senior people in the party who know that he is not functioning on all cylinders.”
Another said: “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.”
Mrs May’s spokesman said: “It would clearly be inappropriate and unacceptable for comments of the sort to have been made or briefed to the press.
“The Cabinet Office is investigating this potential breach of the civil service code fully, just as it would any other.
“If we are able to identify an individual responsible, we will take disciplinary action.”
Cabinet Secretary Sir Mark Sedwill wrote to Mr Corbyn yesterday, offering him a meeting to discuss his concerns.
A date is yet to be set.
Mr Corbyn had called for an inquiry to be conducted independently of the Cabinet Office.
He wrote to Sir Mark, saying: “This matter has inevitably undermined confidence in the principle of civil service neutrality, which is integral to the healthy functioning of our democracy.
“For there to be trust in any investigation, there need to be assurances on its scope and independence.
“In the light of this, I would urge you to ensure that there is a speedy and thorough independent investigation, rather than one carried out by the Cabinet Office.”