“He made a statement so that he could be free to cavort without raising eyebrows,” said a source close to the couple.

Budd made several attempts to reconcile but was stymied because Israel said he was interested only if he could “sleep with other women,” the source told The Post.

Israel, 56, chairman of the powerful Democratic Congressional Campaign Committee, refused to say why he hasn’t filed for divorce and dismissed other questions.

“These allegations are untrue, laughable at best and clearly a political stunt two days before an election,” his spokeswoman said.