Francis had urged for clemency saying it would "give clearer witness to the value and dignity of every person's life".
In a letter from his US diplomatic representative to Oklahoma, governor Mary Fallin, the pontiff said if she called off the execution it would be an "admirable and just act of clemency".
Richard Glossip was due to be killed on Wednesday night for the 1997 killing of an Oklahoma City motel owner.
He has long maintained his innocence and claims he was incriminated by another man, who avoided the death penalty by testifying against Glossip.
Glossip told reporters he was standing in a holding cell a few feet from the Oklahoma state death chamber when he received the news minutes before the scheduled injection.
Oklahoma governor Mary Fallin delayed the punishment after prison officials said one of the three drugs they had received to carry out the injection was the wrong one.
Attorney general Scott Pruitt's office said the reason for the mix-up was unclear, and the Corrections Department director refused to take questions.
A lawyer for Glossip said the incident shows more public oversight of executions is needed.
