His sister, Regina Jackson, who had begged Gov. Phil Bryant to stop the execution, said Tuesday that request was denied.
"He had already made his decision," Jackson said. "He handed it down this morning."
Jackson's two daughters were killed in the attack. She and the parents of the other slain children had met personally with Bryant on Monday.
The governor's office had said Monday that Bryant was reviewing the case. It could not immediately confirm or deny Jackson's statement about a decision Tuesday.
The children who died that day ranged in age from 2 to 5. Another child was left paraplegic and recently died.
Court records say Jackson was looking for money when he went to his mother's Leflore County home on Nov. 1, 1990.
His mother was at church, but Jackson's adult sister, Regina Jackson, was there with two daughters and four nieces and nephews.