Officials said the men, who lived in adjoining cells, drilled a hole through the steel wall at the back of their cells and walked onto a catwalk. They then climbed down and used the tools to drill through a maze of pipes and tunnels before exiting through a manhole on a nearby street, officials said.

Anthony J. Annucci, the acting commissioner of the State Department of Corrections and Community Supervision, said that officials did not know how the inmates acquired the tools. The prison’s tools had been accounted for on Saturday afternoon, he said, but officials were investigating whether the inmates could have gotten tools from outside contractors doing construction at the prison.

Officials were also trying to find out how the inmates knew their way out, he said.

“It may have been over a period of time,” he said. “It may have been trial and error. We don’t know.”

Mr. Cuomo said the inmates had used decoys made from sweatshirts to make it look like they were asleep in their beds, deceiving corrections officers who check on them every two hours.

Image Richard Matt Credit... New York State Police, via Associated Press

The discovery prompted an immediate lockdown of the prison, which remained in effect late Saturday.

Officials said more than 200 law enforcement officers were involved in the search, along with helicopters, K-9 units and bloodhounds. Maj. Charles Guess, the State Police commander of the region, said the police and prison officials were conducting a full investigation with local and state authorities, as well as the Federal Bureau of Investigation and the United States Marshals Service.

The police described Mr. Matt as 6 feet tall and weighing 210 pounds. He has black hair and hazel eyes, officials said. He has a tattoo on his back that says “Mexico Forever,” hearts tattooed on his chest and left shoulder and a Marine Corps insignia tattooed on his right, according to the police.