With the governor's apparently unprecedented intervention, Phillips' execution is on hold until July 2, The Columbus Dispatch reported.
Kasich said he wanted to give medical experts time to "assess whether or not Phillips' non-vital organs or tissues can be donated to his mother or possibly others."
"Ronald Phillips committed a heinous crime for which he will face the death penalty. I realize this is a bit of uncharted territory for Ohio, but if another life can be saved by his willingness to donate his organs and tissues then we should allow for that to happen," Kasich said.
The postponement came the day before Phillips was scheduled to be executed by lethal injection at the Southern Ohio Correctional Facility near Lucasville.
Richard Dieter of the Death Penalty Information Center in Washington said it apparently is the first time in the United States an execution has been stopped to permit an inmate's organs to be harvested, the Dispatch said. He said a Delaware inmate who didn't have an imminent death date was allowed to donate his organs.
Phillips, 40, faces the death penalty for the 1993 beating, rape and murder of Sheila Marie Evans, the 3-year-old daughter of his then-girlfriend.
Kasich said if Phillips is found to be a "viable donor" to his mother or possibly others awaiting transplants of non-vital organs, such as kidneys, the procedures would be performed and then he would be returned to death row to await his execution in July.
Phillips, who had no legal appeals left, had been moved from the Chillicothe Correctional Institution to the Lucasville prison Wednesday morning in preparation for his execution. The newspaper said he had ordered, but didn't eat, what was to have been his last meal -- a pizza with mushrooms, onions and double cheese, spaghetti, corn chips, Dr. Pepper, rocky road ice cream and Oreo cheese cake.