LOS ANGELES (AFP) – Film star turned politician Arnold Schwarzenegger admitted to fathering a lovechild with a staff member which he kept secret for a decade, until its disclosure torpedoed his marriage.

The former bodybuilder's estranged wife Maria Shriver, a daughter of the Kennedy political dynasty, reacted by asking for privacy during a "painful and heartbreaking time," while their children rallied round the family.

A power couple married for 25 years, Schwarzenegger and Shriver announced their separation last week, four months after the former "Terminator" star left office as California governor in January.

They gave no reason for the split at the time, but on Tuesday Arnie revealed he had told his wife about the child he had fathered with another woman, a long-term member of the couple's household staff.

"After leaving the governor's office I told my wife about this event, which occurred over a decade ago," said Schwarzenegger, 63, "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," he said in a statement to the Los Angeles Times.

Shriver, 55, who moved out of the couple's Brentwood mansion earlier this year, appealed for privacy.

"This is a painful and heartbreaking time. As a mother my concern is for the children. I ask for compassion, respect and privacy as my children and I try to rebuild our lives and heal," said the 55-year-old.

The Times did not give the name of the woman or her child to protect their privacy, but said she retired in January of this year after working for the couple for 20 years.

She received a severance payment and "left on good terms" with the couple, the paper said. Other online media were quickly on the hunt for the woman and child, who one report said was an 11-year-old boy who resembles Schwarzenegger.

It was not known how the Austrian-born actor managed to keep the child secret, while the woman remained on their joint staff -- and while he continued to support the child financially, according to the LA Times.

In announcing their separation last week, Schwarzenegger and Shriver said they were taking time to "work on the future."

A few days later Schwarzenegger said they still loved each other, and were taking "one day at a time," hinting at possible reunion -- but reports suggest Shriver is determined to move on.

"We're very fortunate that we have extraordinary children. We're taking one day at a time," he added, in comments late Tuesday at a ceremony to receive an Israeli honor.

It is not the first time the marriage has been strained by Schwarzenegger's relations with other women: it came under the spotlight notably during the 2003 election which he won, amid reports of his history of groping women.

Shriver, a former TV journalist, defended him at the time, and has stood by his side during his seven years at the helm of the Golden State, a term that ended when Jerry Brown succeeded him four months ago.

The couple, who met in 1977 and married in 1986, have four children, aged between 14 and 21.

Patrick Schwarzenegger, 17, tweeted Tuesday: "Some days you feel like shit, some days you want to quit and just be normal for a bit, yet i love my family till death do us apart."

Since January Schwarzenegger has started to return to show business, unveiling plans for a "Governator" comic book and animated TV show, and reportedly signing for a new film in the "Terminator" series.

But his latest bombshell revelation has prompted reaction among at least one gubernatorial peer.

Former Michigan governor Jennifer Granholm tweeted: "Another guy guv admits 2 cheating on his wife. Maybe we need more women governors.

"Guys: keep ur pants zipped, for Pete's sake."