The emergency was due to expire at the end of this month, Italy's ANSA news agency reported.
The extension "is necessary to ensure the successful completion of the complex operations of removing and transferring the ship," a cabinet statement said.
Workers are still working to clean wreckage from the area in time for Giglio's summer tourism season.
Francesco Schettino, the captain of the ship, is facing possible indictment for multiple counts of manslaughter, abandoning his post before the evacuation of all 4,200 passengers and crew had been completed and failing to communicate properly with the maritime authorities. Schettino in turn is suing the Costa Crociere company for alleged unfair dismissal