District Court Judge Patricia Parrish referred to a 1992 Supreme Court decision when she said the state Court of Criminal Appeals must decide whether to grant stays of execution.
Two death row inmates with executions scheduled for later this month are challenging the state over the drugs used to carry out the death penalty.
State lawyers earlier Monday filed an objection stating Parrish has no jurisdiction in the case.
Susanna M. Gattoni, one of the lawyers for Lockett and Warner, said her office would appeal Parrish's decision with the Oklahoma Supreme Court within 24 hours.
Parrish said, however, that she or another civil judge could handle the death row inmates' challenge to the state's execution procedure because the Court of Criminal Appeals does not have jurisdiction to rule in a civil matter. Clayton Lockett and Charles Warner have sued the Oklahoma Department of Corrections to learn more about the drugs that would be used to execute them.
Gattoni said substandard or compounded pentobarbital could leave inmates fully conscious as drugs to paralyze them and stop their heart are administered.
Lockett is scheduled for execution on March 20 and Warner on March 27. The state will continue to move forward with execution procedures until told otherwise, said Jerry Massie, a spokesman for the Oklahoma Department of Corrections.