Post, who gained close to 200 pounds (14 stone) on death row in the US, is trying to stave off execution for the 1983 killing of a motel clerk during a robbery.
State officials say Post (53) can be humanely executed under both Ohio's usual method and the backup procedure of injecting the lethal substance into the muscle.
Post has not presented "sufficient evidence demonstrating that his obesity or other physical conditions will present a substantial risk that his execution cannot be conducted in a humane and dignified manner", Assistant Attorney General Charles Wille said.
A federal judge in Columbus will hold a hearing on Post's claim later this month.
Post weighed 18 stone around the time he was moved to death row in 1985. His weight has gone up and down behind bars, and at one time he lost 10 stone.
But knee and back problems have made it difficult to exercise, his lawyers say. They also say Post's request for gastric bypass surgery was denied, he has been told not to walk because he might fall, and severe depression has contributed to his inability to control how much he eats.