SYDNEY, Australia — James Packer, a colorful Australian billionaire who has found himself embroiled in a corruption scandal involving Israel’s prime minister, has resigned as a director of Crown Resorts, the casino company that is a source of much of his wealth.

In a statement, Crown cited “personal reasons” for his departure without giving further details. But Consolidated Press Holdings, an investment company owned and controlled by Mr. Packer, said in a statement that “Mr. Packer is suffering from mental health issues.”

“At this time,” the company said, “he intends to step back from all commitments.”

Mr. Packer is one of Australia’s richest men, a globe-trotting billionaire who had been engaged to Mariah Carey, formed a film-production company with Brett Ratner in Hollywood — and most recently became entangled in a corruption investigation involving Prime Minister Benjamin Netanyahu of Israel.

According to the police in Israel, expensive cigars, jewelry and pink champagne flowed into the prime minister’s official Jerusalem residence — and one of the patrons was Mr. Packer, who has said he was only giving Mr. Netanyahu what he demanded.