The couple announced in a joint statement May 9 that they had separated after 25 years of marriage. The Times reported Tuesday that Shriver moved out of the family`s Brentwood mansion earlier this year after Schwarzenegger acknowledged the child is his.
"After leaving the governor`s office I told my wife about this event, which occurred over a decade ago," Schwarzenegger said in a statement issued to the newspaper. "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 apologized 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," the statement concluded. "While I deserve your attention and criticism, my family does not."
A spokesman for Schwarzenegger did not immediately return a phone call and e-mail from The Associated Press early Tuesday. A spokesman for the former first lady told the Times she had no comment.
The Times did not publish the former staffer`s name nor that of her child but said the staff member worked for the family for 20 years and retired in January.
In an interview Monday before Schwarzenegger issued his statement, the former staffer said another man -- her husband at the time -- was the child`s father. She said she voluntarily left her position with the couple "on good terms."
When the Times later informed the woman of the governor`s statement, she declined to comment further.