McAuliffe said his team evaluated the trial testimony and concluded that Morva was given a fair trial with information about his mental health available to the jury.
Morva's lawyers have claimed that he was severely mentally ill and suffering from a delusional disorder when he murdered Derrick McFarland, a security guard, and Montgomery County sheriff's deputy Eric Sutphin in 2006.
He is scheduled to be executed at 9 p.m. (1 a.m. GMT) on Thursday with a drug called midazolam, which was introduced to the US lethal injection multi-drug "cocktail" last year after the manufacturer of pentobarbital withdrew that drug from use in executions.
Midazolam's use in executions was called into question after the drug apparently wore off shortly after being administered in at least three cases, including one where the condemned man, Clayton Lockett, began speaking during his execution. The drug is supposed to render people unconscious.
US state lawmakers, EU diplomats and UN experts have urged McAuliffe to grant clemency to Morva, who holds dual US-Hungarian citizenship.
The governor has previously stated he personally opposes executions.