"The security cabinet continues to conduct all actions that will allow the recapture of this criminal," the statement said.
The Government did not say where the operation took place, but the governor of the northwestern state of Sinaloa said special forces had been conducting operations in next-door Durango.
The US television network NBC, quoting security officials, said Mexican marines had approached a ranch by helicopter but were forced back by gunfire.
They later entered the camp on foot but discovered Guzman and his henchmen had fled in all-terrain vehicles. They found medication, two-way radios and the phones used to trace him.
Troops flooded the area, and at first thought they had pinned down Guzman, the billionaire head of the Sinaloa drug cartel, within a 3.2km radius.
However, there has been no sign of him since.
The encounter is the closest the authorities have come to recapturing "El Chapo", who fled the Altiplano prison just 17 months after US-backed marines captured him in the Pacific resort of Mazatlan in Sinaloa after a 13-year manhunt.
He slipped through a hole dug in the shower in his cell and escaped on a motorcycle through a 1.5km-long tunnel equipped with ventilation and lighting, emerging in a house outside the prison.
The escape of such a high-profile figure has been a major source of embarrassment to President Enrique Pena Nieto's Administration.
A new video emerged last week, revealing that loud hammering could be heard coming from Guzman's cell before the audacious escape. It took guards nearly 40 minutes to respond.
More than a dozen prison officials have been detained over charges that they helped him flee.