The Hillary Clinton campaign has moved to debunk what it described as "deranged conspiracy theories" of Donald Trump and his supporters suggesting that Ms Clinton is not physically well and is suffering from brain damage.

Fox News led the attack when presenter Sean Hannity highlighted a stumble on the podium beside vice president Joe Biden this week and speculated about the lasting effects of her supposed "traumatic brain injury" - the brief concussion she had in 2012 after a stomach virus.

"What about some of the weird pauses she has, the coughing fits she has? There are moments when I’m literally watching her and I’m thinking, OK, the facial expressions are odd," said Mr Hannity. "They seem off."

The Clinton campaign has now pushed back against the health rumours for the first time, saying that Mr Trump is peddling conspiracy theories in an attempt to detract attention from his tax returns.

Ms Clinton released her medical records in late July which said she was in "excellent physical condition and fit to serve as President of the United States".

"Hillary Clinton has released a detailed medical record showing her to be in excellent health plus her personal tax returns since 1977, while Trump has failed to provide the public with the most basic financial information disclosed by every major candidate in the last 40 years,” said Jennifer Palmieri, the campaign's director of communications, in a statement.

"It’s time for him to stop using shameful distractions to hide his own record."

The extraordinary exchange is a symptom of the negative campaigning that has been a feature of a White House race between two candidates with record high unfavourability ratings and who want to secure their respective bases.

Mr Trump claimed he also released his own health record last month.

The letter was condemned as unreliable and written by a specialist physician who deals with digestive issues.

The letter read: "If elected, Mr Trump, I can state unequivocally, will be the healthiest individual ever elected to the presidency."

"He says that all of Mr Trump's medical tests are positive," said Vanity Fair's contributing editor, Kurt Eichenwald, on CNN. "That means that everything he was tested for, he has. No competent or real doctor would write this."

Mr Trump has already come under fire for previous "conspiracy theories", including that president Barack Obama was the founder of terrorist network Isis.