Gov. Andrew Cuomo said they may have crossed into Canada or left for another state.
The two men escaped by cutting through steel walls and pipes, and authorities were investigating how they obtained the power tools. Officials gave no details on how the men managed to avoid detection.
The prison, called "Little Siberia" by locals, houses nearly 3,000 inmates, is surrounded by farmland and forests and is about a 45-minute drive from Montreal.
David Sweat, 34, was serving a sentence of life without parole for the 2002 killing of a sheriff's deputy. Richard Matt, 48, had been sentenced to 25 years to life for kidnapping, killing and dismembering his former boss in 1997.
Authorities set up roadblocks and brought in bloodhounds and helicopters. Hundreds of law enforcement officers fanned out around the prison, about 32 kilometers south of the Canadian border.
Prison officials found the inmates' beds inside the 150-year-old Clinton Correctional Facility stuffed with clothes on Saturday morning in an apparent attempt to fool guards making their rounds. On a cut steam pipe, the prisoners left a note containing a crude Asian caricature and the words "Have a nice day."
Officials said the inmates cut through the steel wall at the back of their cell, crawled down a catwalk, broke through a brick wall, cut their way into and out of a steam pipe, and then sliced through the chain and lock on a manhole cover outside the prison.
Cuomo said investigators were confident the men obtained the tools inside the prison. Acting Corrections Commissioner Anthony Annucci said an inventory of prison tools had so far shown none missing and he was in contact with contractors who were doing or had done work at the prison.
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