Arnold Schwarzenegger had fathered a child over 10 years ago
Maria Shriver - who was married to the `Terminator` actor for 25 years and has four children, Katherine, 21, Christina, 19, Patrick, 17, and Christopher, 13, with him - moved out of the family`s Los Angeles mansion earlier this year after Arnold admitted paternity of the child, whose mother worked with the family for 20 years before retiring in January.
Arnold - the former Governor of California - said in a statement released to the Los Angeles Times newspaper: "After leaving the governor`s office I told my wife about this event, which occurred over a decade ago. I understand and deserve the feelings of anger and disappointment among my friends and family. There are no excuses and I take full responsibility for the hurt I have caused. I have apologised to Maria, my children and my family. I am truly sorry.
"I ask that the media respect my wife and children through this extremely difficult time. While I deserve your attention and criticism, my family does not."
Following the news of the couple`s shock split earlier this month, Arnold, 63, revealed he was taking the break-up "one day at a time".
He said: "We both love each other very much. And we`re taking it one day at a time. The bottom line is we want to thank all the people for their great, great support.
"I just spoke to Maria an hour ago before I came here. We both were saying the same thing - we`re extremely blessed to be surrounded by so many wonderful people, by so many wonderful friends."