The reputed underboss of the New England mafia, awaiting trial on bribery charges, is asking a federal judge to release him from home confinement for two hours a day so he can exercise.

A lawyer for Carmen “The Cheeseman” DiNunzio filed a petition on Tuesday saying a doctor recommended 30 minutes of “sustained aerobic exercise” per day. The 51-year-old DiNunzio, who weighs some 400 pounds, said he’s battling health ailments, including diabetes and heart disease.

DiNunzio also sought permission to periodically spend the night at a hospital for treatment of sleep apnea, the disorder in which breathing is disrupted during sleep.

His lawyer, Anthony Cardinale, says federal prosecutors have not objected to the request.

DiNunzio has been out on $20,000 bail since his May indictment. He is accused of trying to bribe an official to win a lucrative contract on the huge Massachusetts highway project known as the Big Dig.

He is called “The Cheeseman” because he owns a cheese shop in Boston’s North End.