Turkey's state-run TV earlier on Thursday quoted the country's foreign minister Ahmet Davutoglu as saying that NATO would soon take control of the operation.
"Compromise has been reached in principle in a very short time," Davutoglu said. "The operation will be handed over to NATO completely."
Turkey expressed reservations about the NATO military intervention in Libya and sought assurances that it would not go beyond the goal of protecting civilians.
France also objected to plans to hand the mission over to NATO.
On Wednesday the NATO council approved the alliance's participation in a mission to ensure an arms embargo against the country using 16 war ships and submarines.
The UN Security Council imposed a no-fly zone over Libya on March 17, allowing "all necessary measures" to protect civilians from Muammar Gaddafi's attacks on rebel-held towns.
The operation to enforce the no-fly zone, codenamed Odyssey Dawn, is conducted jointly by 13 states, including the United States, Britain and France.
Western warplanes have flown more than 300 sorties over the North African country and fired 162 Tomahawk missiles in the UN mission.