Prominent Israeli journalist Ari Shavit, whose book "My Promised Land" became a bestseller in the United States, said Sunday he was resigning from his newspaper and television posts after sexual harassment allegations.

The allegations against Shavit have caused waves in Israel, where he is well-known as a columnist for leftwing newspaper Haaretz and a commentator for privately owned Channel 10 television.

The controversy began after US journalist Danielle Berrin published a piece on October 19 for the Los Angeles-based Jewish Journal about a meeting with Shavit for an interview in 2014.

At one point, he "lurched at me like a barnyard animal, grabbing the back of my head, pulling me toward him," she wrote.

Berrin did not name Shavit in her piece, but clues in the story led to suspicions it was him. 

He later acknowledged having met Berrin and apologised, saying he "thought that we had had a friendly conversation that included some flirtation."

A second woman, an anonymous staffer for US-based organisation J Street, has since said that Shavit came onto her and inappropriately rubbed her hand as they had a coffee after she picked him up for an event as part of her job duties.

In a statement on Sunday, Shavit said he took "full responsibility for my actions" and announced his resignation from Haaretz and Channel 10.

"I am ashamed of the mistakes I made with regards to people in general and women in particular," Shavit said, according to Haaretz. 

"I am embarrassed that I did not behave correctly to my wife and children. I am embarrassed about the consequences of what I did." 

Shavit's 2013 book "My Promised Land: The Triumph and Tragedy of Israel" became a New York Times bestseller.