CINCINNATI  Two days after the execution of a convicted rapist-murderer was halted when technicians were unable to inject him with lethal drugs, a federal judge ordered Thursday that the inmate be deposed for a federal lawsuit challenging the constitutionality of Ohio’s lethal injection procedure.

The deposition for the inmate, Romell Broom, is set for Monday, a day before he is scheduled to be executed. His lawyers said they planned to file appeals in state and federal courts on Friday seeking to cancel or at least postpone his execution.

One of his lawyers, Adele Shank, said the appeals would present three arguments that executing Mr. Broom on Tuesday would constitute cruel and unusual punishment. They will contend that seven days is not enough time to recover from the physical and emotional trauma of the failed execution attempt, that Ohio’s lethal injection system in its current form is critically flawed and that lethal injection, in general, is cruel and unusual punishment.

The execution of Mr. Broom, 53, was postponed Tuesday after technicians tried and failed for more than two hours to maintain an IV connection in order to inject him with lethal drugs.