David Blunkett has denied being a hypocrite telling the BBC revelations about his private life do not affect his job as home secretary.
Mr Blunkett says he stands for responsibility and respect
An inquiry is investigating whether the home secretary helped fast-track a visa application for his ex-lover's nanny.
Mr Blunkett insisted he was meeting his responsibilities, saying everyone made mistakes and had frailties.
He said: "I don't think anyone can say I have said one thing in public and done another in private."
Last week, the home secretary won the first round of a High Court battle with his ex-lover Kimberly Quinn for access to her son.
Mrs Quinn wants to give evidence to former civil servant Sir Alan Budd's inquiry into whether Mr Blunkett interfered in the British residency application made by her nanny, Leoncia Casalme.
On Monday, he made a plea for understanding as he denied the revelations about his affair showed he was taking a risk when he spoke about personal responsibility.
"It would be dangerous territory if I wasn't practising what I preach which is to always accept responsibility, always accept the consequences of your actions," he said.
"All of us in our lives have to rely on the support and well-being of others. Sometimes we make mistakes.
"But one thing is absolutely certain, if we don't combine together, if we don't engage with each other, if we don't understand each other's frailty then we really will atomise and the world will fall apart.
"So actually understanding the way in which we pick up the pieces and work together to build a better world is in no way to actually undermine the fact that politicians are just as human as anyone else."
Mr Blunkett declined to comment about his own position, saying the inquiry was under way and the High Court had stressed his right to privacy did not affect his job in improving security and stability.
Asked if he had ever considered resigning during the row, he said he would not even answer that question.
And he rebutted any suggestions of hypocrisy.
"Everything I stand for is about personal responsibility, it's about respect, it's about building cohesive society where you take the consequences of our actions.
"We don't blame other people for what has happened to us but we are able to face difficult decisions, and my job is to help write that large in our community and society so that we have a safer more secure environment in which people can take up the opportunity to make something of their lives.
"And that's what I am going to do."
Mr Blunkett showed his determination to press on with his official duties on Monday when he launched a new initiative to encourage personal safety among teenagers.
Downing Street said Tony Blair's backing had not changed "one iota" since last week.
A new biography of Mr Blunkett quotes him being critical of some other Cabinet ministers in conversations with colleagues.
The book, by Stephen Pollard, says he is disappointed with Education Secretary Charles Clarke for going "soft" on standards and he says Trade Secretary Patricia Hewitt "thinks strategically".
Asked about the comments, Mr Blunkett said he would not comment on "tittle tattle".