A spokesman for Virginia Gov. John N. Dalton said today the governor is not likely to stay the scheduled June 13 execution of convicted murderer Joseph M. Giarratano.

Dalton supports capital punishment and "has not heard from anybody" appealing to him to halt the electrocution, said Paul G. Edwards, the governor's press secretary.

"There's no action for him to take unless there's an appeal," Edwards said. "He supports the death sentence on the books now."

Edwards said he is uncertain what action the governor would take if an appeal if filed. "That's too hypothetical," he said. But, he added, "I can't anticipate anything that might come up, but I can't imagine he would act."

"When they come to get me Friday the 13th, I'll be ready to go," Giarratano, 22, of Ft. Lauderdale, Fla., said last week in an interview with The Norfolk Virginian-Pilot.

"Then the hurt will be over at last. The pain and feelings I can't live with will be ended," said Giarratano, who blames his criminal behavior on psychological problems.

Giarratano, scheduled to become the first person executed in Virginia since 1962, was convicted of the Feb. 4, 1979 rape and murder of a Norfolk teen-ager and her mother, who had given the jobless drifter a room in their home.

"Society will be doing me a favor by putting me out of my misery," he told the newspaper during an interview in his cell, located just 30 feet from the electric chair at the State Penitentiary in Richmond.