Oksanka Grigorieva and Mel Gibson appeared at numerous public events

Actor Mel Gibson is being investigated over claims of domestic violence, Los Angeles police have confirmed.

They said an allegation was being looked into following an interview with the star's Russian ex-girlfriend Oksanka Grigorieva.

But spokesman Steve Whitmore declined to disclose any further details, saying the probe was in its early stages.

The Oscar-winner and Grigorieva have been involved in a custody case over their eight-month-old daughter Lucia.

Irreconcilable differences

Court proceedings concerning the child, Gibson's eighth, have been conducted behind closed doors.

The couple have both obtained restraining orders against each other.

Gibson, 54, who won an Oscar for directing Braveheart in 1995, has not spoken in public about the breakdown of his relationship with 40-year-old Grigorieva.

Gibson pleaded no contest to a drink-driving charge

The actor announced they were together shortly after his wife Robyn filed for divorce in April 2009 after 28 years of marriage.

The proceedings, which were initiated on the grounds of irreconcilable differences, are still ongoing.

The investigation into domestic violence relates to an incident which allegedly took place earlier this year.

It could take a month to complete and the results will be handed over to the district attorney's office who will determine whether to pursue charges.

The Malibu police unit looking into the claims also arrested Gibson in 2006 on suspicion of drink-driving.

The actor later apologised for making anti-semitic comments during his arrest and was given three years' probation.

The charge was expunged from his records last year.