A city inmate escaped Rikers’ jail barge Tuesday, leaped into the East River and is now clinging to life, law-enforcement sources told The Post. 

The 48-year-old detainee climbed a recreation-yard fence at the Vernon C. Bain Center, crawled under razor wire and then jumped five stories into the river at about 11:44 a.m., according to sources and a DOC spokesperson.

Staff threw the man several life rafts but they claim he refused to accept them, internal records show.

When he was pulled out of the water about 10 minutes later by the NYPD’s Harbor Unit, he was unresponsive, sources said.

The man, who was being held for robbery, was transported to Mount Sinai Queens in grave condition, according to sources and the FDNY.

Warren Silverman, who represents the man, said the DOC had not called to inform him what happened even hours after the incident.

“At this point, I don’t know if they bothered to contact anyone,” the lawyer said.

“Once again, their system failed. I mean, he shouldn’t have been able to get to any position where he could have harmed himself, and clearly they dropped the ball, as usual.”

A city Department of Correction rep called the incident an “attempted escape” and said “an investigation is ongoing.”

Deaths in DOC custody are up 40% so far this year compared to the same period in 2022, data show.