Mr Brown strongly denied instructing his advisers to brief against Mr Darling in 2008, after the Chancellor predicted the recession would be the worst for 60 years.
But Conservative leader David Cameron taunted him over the allegation at Prime Minister's Questions, telling MPs that Mr Brown's then close adviser Damian McBride had in fact been "spreading poison" about the Chancellor to journalists.
Challenging the PM to repeat on the floor of the Commons the defence he gave on the GMTV sofa this morning, Mr Cameron said: "Right now, six weeks before an election with a record budget deficit at the end of a long recession, I want to ask why the Prime Minister and Chancellor are at war with each other."
Mr Darling appeared to be pointing the finger at Mr McBride when he told Sky News last night about newspaper reports in 2008 suggesting he was about to be removed from the Treasury: "I'd done this interview and the forces of hell were unleashed."
Asked whether Number 10 was responsible, he added: "Not just them, the Tories as well."
But Mr Brown today told GMTV: "I would never instruct anybody to do anything other than support my Chancellor."
The PM added: "Alistair has been a friend of mine for 20 years, we have worked together, our families know each other. We have worked together all this time and we have huge mutual respect for each other."
And Mr McBride - who quit Number 10 last year over his involvement in an email exchange discussing possible smears against leading Tories - denied that the Prime Minister had ordered him to undermine the Chancellor.
"The idea of Gordon instructing us to brief against Alistair Darling is totally wrong. The idea of me briefing against Alistair Darling is totally wrong," Mr McBride told the BBC.
"The Sunday papers were ringing up and asking us if we were angry with the Chancellor and the answer was no."
Mr Brown and Mr Darling put on a display of unity at Prime Minister's Questions today, arriving together and sitting alongside one another on the front bench.
Hailing Mr Darling as "right on every issue", the Prime Minister told Mr Cameron: "I would rather be defending my Chancellor than be in your position of having to defend your shadow chancellor."
The two men sat so near to one another and whispered so intently as Mr Cameron spoke that the Tory leader joked: "Any closer and they will start kissing!"
Speaker John Bercow threatened to suspend the sitting after rowdy backbenchers made it almost impossible to hear the furious exchanges.
Referring to the weekend's row over claims that Downing Street staff rang an anti-bullying helpline, the Speaker said if MPs did not stop shouting, "I might have to ring some sort of helpline myself".
The National Bullying Helpline announced today that it was suspending its phone operation and chief executive Christine Pratt was "prepared to resign if necessary" after the storm over her allegations.
The charity said it was "considering its future" after four patrons - including Conservative MP Ann Widdecombe - quit in protest at what they saw as a breach of Mrs Pratt's duty of confidentiality.
Meanwhile, Cabinet Secretary Sir Gus O'Donnell told MPs that he had never given the Prime Minister a warning about his treatment of staff, as claimed in a book by political commentator Andrew Rawnsley.
"I never talked to the Prime Minister about his behaviour in relation to bullying No 10 staff, but of course I talk to the Prime Minister about how to get the best out of his civil servants," Sir Gus told the House of Commons Justice Committee.
"I haven't called for investigations, I haven't given verbal warnings."
The most senior civil servant in 10 Downing Street, permanent secretary Jeremy Heywood, confirmed that he spoke to Mr Rawnsley ahead of the publication of his book, but insisted he did not discuss the Prime Minister's character with him.
Speaking on Mr Heywood's behalf, Mr Brown's spokesman said: "He did not speak to Mr Rawnsley about the Prime Minister's working style or behaviour.
"He talked about the excellent role the Prime Minister played in helping the UK through the international crisis in 2008."
Speaking to GMTV, Mr Brown denied being a bully but admitted his actions could be viewed as those of a "hard taskmaster".
"I get angry sometimes - doesn't everybody?" said the Prime Minister. "I get impatient, I am driven to do the things. When I came into the job, I said look, I will try my utmost and I challenge people, I ask them to do the best they can.
"Actually, we work in an open plan office, we are a sort of family in Downing Street and like every family there are issues that come from time to time, but we have got a great working environment and we get things done."
He added: "In my job you have got to get things done, you have got to push people, you have got to challenge people. You don't solve a world recession by being a shrinking violet."
Mr Darling admitted last night that he and the Prime Minister had "bad days", but insisted they were outnumbered by good days.
"Of course Gordon and I have some very robust exchanges," he said.
"I can't imagine any healthy relationship between a prime minister and a chancellor where they don't have differences of opinion from time to time."
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