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Rudy Giuliani’s wife told The Post on Tuesday that her estranged husband is lying when he says he hasn’t been having an affair — and insisted that the illicit relationship began before they were separated.

As The Post exclusively reported Tuesday, Giuliani has been cheating on wife Judith Nathan with married New Hampshire hospital administrator Maria Rosa Ryan, according to sources.

Giuliani denied the affair to The Post, although he added that the dinner and movie he shared with Ryan at a posh spa March 29 — five days before Nathan filed for divorce — occurred when he “was in effect separated.”

Nathan shot back in a statement, “My husband’s denial of the affair with the married Mrs. Ryan is as false as his claim that we were separated when he took up with her.”

There was no legal filing for a separation before Nathan filed for divorce.