Mr Livingstone later offered an olive branch to Mr Johnson by closing an attack website aimed at the Mayor as he warned the election race was getting "out of hand". He said:
"Those of us who are leading candidates in this election have a duty to the electorate to rein it in and direct it to the issues at stake for Londoners.
"I suggest to Boris Johnson therefore that he and I work together to raise the tone and spirit of this election."
A spokesman for Boris Johnson has said: "Boris Johnson has repeatedly made clear he pays all taxes in full. Ken Livingstone knows this because he has been personally told by Boris Johnson during a private conversation at a business hustings just two weeks ago.
“Mr Livingstone repeated these false claims today, knowing full well they are not true, in a desperate attempt to avoid answering serious questions over his own tax affairs".
Boris Johnson said: "Of course the real point is not about my tax arrangements. It is about the hypocrisy of a man who for years has railed against those who use special arrangements to reduce their tax and who has then been caught – bang to rights – doing the very same thing himself."
A spokesman for Ken Livingstone said: "Boris Johnson lost his temper because he lost the debate - he talked about cable cars, not cutting fares and the squeeze on Londoners."
The row continued off-air when a furious Mr Johnson swore at his Labour opponent.
Travelling up to the roof terrace to be photographed, the Mayor shouted at Mr Livingstone "it's all f****** lies, it's all f****** lies".
Ken Livingstone and Boris Johnson clashed furiously over their tax arrangements in the first live debate ahead of the mayoral elections.
Mr Johnson denied suggestions he had used a company to channel his media earnings to avoid paying income tax - a claim that he has levelled at his Labour opponent.
Mr Livingstone accused the mayor of having "the same arrangements" for dealing with his media earnings as he had, insisting he had used a company called Finland Station.
Mr Johnson called the claim "lies", adding: "I have never used a company to minimise my tax.
"There was a TV production company which I was briefly a director of but I certainly never ... I have always paid full income tax."
Boris Johnson and Ken Livingstone were involved in a furious row in the lift after the London mayoral debate at LBC Radio. Sources say Johnson and Livingstone were "nose to nose" and Johnson 's face was "red with rage".