Work and Pensions Secretary David Blunkett has insisted he will not resign, telling The Star newspaper in Sheffield: "I have done nothing wrong."
The Lib Dems want Mr Blunkett to make a personal statement
Letters show he was warned three times to seek advice about taking jobs while out of Cabinet, but failed to do so.
As a result, says standards watchdog Sir Alistair Graham, Mr Blunkett had broken the ministerial code of conduct.
The Tories have written to Tony Blair after it emerged Mr Blunkett took a third job without seeking advice.
But Mr Blunkett told The Star newspaper on Tuesday: "I have done nothing wrong at any stage."
The row centres on Mr Blunkett's appointment as director of DNA Bioscience before May's general election, while he was out of the Cabinet, and his holding of shares in the firm.
He was in the job for a fortnight, resigning when he was appointed work and pensions secretary.
The Cabinet minister said on Monday he had decided to ask his sons to dispose of the shares - reported to be worth £15,000 - to avoid "continuing misinterpretation of the position".
Mr Blunkett told The Star: "The pressure is not continuing. The prime minister has made his decision and, no matter what the Conservative Party want, I am not resigning.
"This is a straight political battle with the Conservative Party and their allies in the media, and decency.
"I have done nothing wrong at any stage. I have been transparent about everything I have done."
'Lost the plot'?
Conservative Sir Malcolm Rifkind said it was a question of judgement and Mr Blunkett had "lost the plot".
Senior Labour MP Ian Gibson said if he was Mr Blunkett he would resign.
But Downing Street continues to support Mr Blunkett, with Tony Blair's official spokesman saying: "David Blunkett has accepted he made a mistake. The question is, does that mistake stop him doing his job? The prime minister's judgment is that it does not."
The official ministerial code suggests that former ministers should seek the advice of the advisory committee on business appointments before taking up other jobs.
However, on Tuesday it emerged that Mr Blunkett had taken on a third job during the same period out of office, earning between £15,000-£20,000 as an adviser to World ORT, an international charity, without taking advice.
Shadow Commons leader Chris Grayling has written again to Mr Blair about Mr Blunkett's conduct, which he said "is getting beyond a joke".
But the prime minister's spokesman said the so-called third job was covered by "the same mistake" that Mr Blunkett had "made with the other two jobs".
The spokesman said Mr Blunkett had "shown the integrity" the prime minister expects.
The Liberal Democrats want Mr Blunkett to make a personal statement in the Commons, so that he can answer questions about his business dealings.
Three letters detailed in Tuesday's Times show Lord Mayhew, chairman of the Advisory Committee on Business Appointments, spelt out to Mr Blunkett before he took the DNA Bioscience directorship the fact ex-ministers should consult his committee for advice before taking up jobs.
Sir Alistair Graham, chairman of the committee on standards in public life, said "undoubtedly there was a breach of the ministerial code" because Mr Blunkett had not sought that advice.
But Trade Secretary Alan Johnson said the affair did not warrant a resignation.
Mr Johnson told BBC News 24: "David Blunkett is a talented politician, a thoroughly decent man, it's about time the open season on David Blunkett finished and he was allowed to get on with his job."
Mr Blunkett stepped down as home secretary last year over claims his office had fast-tracked a visa application for his lover's former nanny.
Is it time to end the row over Blunkett's business dealings? Send us your comments on the form below
Like many politicians, Blunkett's time is up, he has lost the judgement he had, judgement that is always undermined through the complacency of being in power and being patronised by those around you.
Brian Hawkins, Woodbridge Suffolk
The man has no honour, he's used his position too many times for his own benefit, that's not what he was voted in to do. He should resign.
Colin Scott, Barcelona, Spain.
Resign. This seems to be another political game by the two major parties. They pick a small problem and keep our attention away from the real problems - economy, unemployment, war on Iraq, etc. You have to remember that it was the conservatives who supported the war!
Whatever happened to 'once bitten twice shy'. If he is not humble enough to learn from his previous mistakes then he is not fit for high office.
Unfortunately the British people are getting what we voted for at the last election. A government who see no need to apologise for anything they do, provided they think they were right when they did it, that makes it OK. Is it any wonder we now live in a society where people are not prepared to accept responsibility for the consequences of their actions when we are set examples like this from the very top.
Mike Beavis, Belper, Derbyshire
He should resign.
Syd Fogarty, St Albans Herts
The Ministerial Code is voluntary? Will we see the same MPs make it law? I doubt it.
Rafez Noorullah, Northants, UK
Ministers & MPs have rules to follow. He didn't follow them so he should resign.
Brian Willey, Newport, South Wales
The Advisory Committee on Business Appointments was set up to ensure there could be no possibility of ministers benefiting personally through industry from decisions they took in their previous Public Office. The Directorship of the DNA testing company has no relevance to his previous office as Home Secretary. Furthermore, the wording of the Ministerial Code states "On leaving office, ministers should seek advice from the independent Advisory Committee on Business Appointments". If it were a mandatory requirement, it would start "On leaving office, ministers MUST..." A storm in a tea-cup !
Peter Rayner, Brighton, Uk
Blunkett should go. Too often we hear from him that in hindsight he should have done this, that or the other after he is been involved in yet another scandal. He gives the impression that he feels he is above the rules and it is dangerous to have that sort of man in such a powerful post.
Mark Walpole, East Horsley, Surrey
I think he should resign. He seems unable to stop himself from getting into difficulties and you have to seriously question his judgement as a result.
Terry Bell, Swindon, UK
Blunkett has proved he is an "unsafe pair of hands" on countless occasions. Because of this and his arrogance he should resign! Its very worrying about Blair's judgement allowing Blunkett back.
Mike Pearce Norwich, Norwich England
I think everyone should just leave David Blunkett alone. It was bad enough he had his private live dragged through the press. This current affair has nothing to do with anyone. He has not profited from the shares and has not spent taxpayers¿ money.
Blunkett is in a position of power and control over our lives and liberties as Home Secretary and Works and Pensions Minister, yet he has consistently failed to read the small print of his own employment contracts. He abused his benefits by giving rail tickets to his mistress, and now this. He has an arrogant disregard for the need to follow the letter of the law. I can't accept a government minister who is so free and easy with his own rules.
Michael Kilpatrick, Cambridge UK
Just another sleazy politician! Whether he has done anything procedurally improper or not, it smells to high heaven!
I think Blunkett needs to get off his high horse, admit he has made a good few serious mistakes and leave the cabinet with some dignity. He continued arrogance that he has not done anything wrong is a damaging characteristic for such a senior member of the government.
Ayesha, London, UK
As a lifelong Labour voter I am disturbed by Tony Blair's attitude to this matter. Surely after what has gone on before Mr Blunkett should act within the rules more than ever. He should be squeaky clean otherwise he is a target for cheap pot-shots from the opposition. He is far too clever a man for anyone to believe he was acting naively over his directorship. He should step down now. This matter is not going to go away.
Ian Hepworth, Pickering, North Yorkshire, UK
Mr Blunkett should resign, not because of the current argument but because he has repeatedly made similar errors of judgement that demonstrate his complete inability to understand the meaning of the word 'honourable.'
Kate Corwyn, Exeter
David Gunthorpe, Cardiff
This is just another example of our politicians seeking to enhance their positions at a cost of falling standards which in turn encourages less privileged persons take what they can without regard to others. What future western civilisation?
Derek Lamb, Oxford, England