Mr Robinson publicly reacted after his wife revealed she had a "brief affair" last year and tried to kill herself.
"So great was my guilt and regret that I tried to take my own life ten months ago", she said in a statement to the media.
Read Ken Reid's blog: Family affairs
An emotional Mr Robinson spoke of his anguish to a select number of journalists who were invited to the family home on Wednesday.
"My first knowledge of Iris' inappropriate relationship came at midnight of March 1 last year, the night that she tried to take her life", he said in a remarkable interview in which he bared his soul on what has been a ten-month nightmare for him and his family.
"You will appreciate how devastated I am over what I have learned from Iris. This has been the most difficult period of my life and I have been hurt by what has happened. I feel the pain of it every day."
Mr Robinson admitted his "immediate impulse" was to walk away, but said he decided to stand by his wife and make every effort to save his 40-year marriage.
"I set her inappropriate behaviour against 40 years of bringing up our children, 40 years of selflessly giving me the space to pursue my beliefs, and facing public pressure," he said.
"In my view, (Iris) would be less likely to recover if I had left."
Mr Robinson claimed the couple first considered going public about the affair last November, but decided against the move because of medical advice that his wife would not have been able to cope with the consequences.
Mr Robinson described the last year as "a very painful time for my family".
"I ask that (the media) respect our personal privacy while we seek to rebuild our lives."
'Guilt'
Iris Robinson has been suffering from what she calls "serious mental illness" and resigned from political life at the end of last month.
"I fought with those I love the most- my children and friends; saw plots where none existed and conducted myself in a manner which was self-destructive and out of character," the former Strangford MLA said.
"I lost control of my life and did the worst thing that I have ever done. Over a year ago I was involved in a relationship."
Ms Robinson revealed the affair began innocently when she gave support to someone following a family death.
The 60-year-old mother-of-three said that she encouraged friends to assist him financially for a business venture.
To her regret she said the relationship later developed into a brief affair.
"It had no emotional or lasting meaning but my actions have devastated my life and the lives of those around me," she said.
"I do not deserve a second chance but I have been given one. Nothing is more important to me."
Ms Robinson said she was "completely ashamed" and "deeply embarrassed".
"I let down thousands of people who placed their faith in me and though my medical condition was a factor I was not, at this time, true to the values I professed," she said.
Finance
During the interview Peter Robinson denied his financial affairs were under investigation.
"In all of my public life I have acted in the most professional and ethical way", he said.
"I've heard all sorts of nonsense and rumours of the last number of days. One indicating that I lost £3m in shares - absolute rubbish."
"I am absolutely certain that everything that I have done has been done as it should. I know of no other allegations that have been made against me that suggest otherwise."
Mr Robinson also insisted he will not be resigning as First Minister.
"I want to assure the wider community that I have at all times sought to carry out my public duties, and I will continue to discharge those responsibilities", the DUP leader said.
"I will be meeting with Martin McGuiness to discuss how we might make real progress, I want 2010 to be a better year for all of us."
On Wednesday night Mr McGuinness said nobody watching the TV interview could fail to be moved by obvious hurt and pain being experienced by the Robinson family.
He said: "Despite Peter's public role, he is entitled to privacy as he and his family seek to deal with this matter. I wish them well as they seek to rebuild relationships away from the public glare."
DUP deputy leader Nigel Dodds passed his best wishes to the Robinson family on behalf of the rest of his party colleagues.
"He has demonstrated a level of bravery and courage that very few in public life possess", he said.
"He is the undisputed leader of Unionism and we all offer our full and total support at this time."