The MTA urges prosecutors to seek temporary bans against recidivist subway criminals from the system — but only lifetime prohibitions will do the trick, police sources argue.

Even though the sick crimes occur on MTA property, it’s largely in the hands of the legal system to ban anyone from the system, whether temporarily or for good.

And despite the MTA beseeching prosecutors and parole officers to ask for and enforce short-term subway bans as conditions of repeat offenders’ probation or parole terms, many of the serial sex criminals refuse to obey the toothless orders or simply wait until they expire, sources said.

“NYC Transit is committed to ensuring public safety and encourages prosecutors to use every tool available including seeking strict sentences and court orders to protect our customers and employees from recidivist offenders,” the agency said in a statement.

Asked whether it would support permanently banning the worst of the worst, the MTA did not respond.

The NYPD has long pushed for lifetime bans for recidivists, which would allow cops to treat violators who set foot on MTA property like trespassers and arrest them on sight.

“Multiple stores do that, where if you’ve been arrested for shoplifting, they’ll take a picture of you and say, ‘Stay out of our store,’ ” explained one high-ranking department source. “If they do come back, they’ll get arrested.”

But pushes by the department for permanent bans have stalled in the face of arguments that even repeat sex criminals such as Ronald Dudley, charged last month with exposing himself and rubbing against a 9-year-old girl aboard a 7 train, deserve access to public transit.

“I’m sure this will open up a discussion on, ‘Doesn’t everyone have a right?’ ” predicted the source. “But doesn’t that 9-year-old have a right?”