Israel’s prime minister scammed his country’s revered Holocaust memorial, a charity for disabled children and other groups out of $100,000 in a brazen double-billing scheme, investigators said yesterday.

They said Ehud Olmert personally ran the fraud and used the money to finance lavish family trips abroad.

One law-enforcement official said Olmert would have been arrested already if he weren’t prime minister.

The dramatic new charges sharply expanded the three-month probe and greatly increase the likelihood that Olmert will be indicted and forced from office.

Police revealed the new allegations after questioning the prime minister, for the third time, yesterday in what they described as a “tense” two-hour confrontation.

They turned the focus of the investigation to trips that Olmert took with his wife, Aliza, and children before he became prime minister in 2006, when he was mayor of Jerusalem and a cabinet minister.

Olmert told detectives he financed the vacations through frequent-flier miles he accrued on his many foreign trips, including speaking tours of the United States.

But investigators suspect the real source was nearly $100,000 he amassed in a special bank account arranged with an Israeli travel agency, Rishon Tours.

They said Olmert often spoke abroad on behalf of groups like the Yad Vashem Holocaust memorial, a charity for mentally disabled children, and a support group for Israeli Defense Force soldiers.

But he would have Rishon Tours send the same bill for his trips to each of the groups, as if they were the only one paying.

A senior police officer with the national fraud unit said Rishon Tours “acted like a bank branch for the Olmert family.”

Police raided the Rishon Tours offices recently and seized documents.

Olmert’s spokesman said the prime minister “is convinced that he is innocent of any wrongdoing and firmly believes that, as this investigation continues, that innocence will become apparent to all.”

Supporters said the police were making the investigation a “personal campaign” to oust Olmert.

But an Israeli newspaper quoted a law-enforcement source as saying “anyone else would have been arrested” by now.

Olmert has said previously he would step down if indicted.

Until now, the most damning evidence had come from Long Island businessman Morris Talansky, who tearfully testified in May that he tried to help Olmert’s political career by giving him $150,000 in cash-stuffed envelopes. With Post Wire Services

andy.soltis@nypost.com