"It was an elaborate plot," Cuomo said after joining law enforcement authorities to retrace the prisoners' escape route from the Clinton Correctional Facility in the town of Dannemora in the Adirondacks.
He said Richard Matt, 48, and David Sweat, 34, are "two dangerous individuals."
Sweat is serving a sentence of life without parole after he was convicted of first-degree murder for killing a Broome County sheriff's deputy in 2002. Matt is serving a sentence of 25 years to life for the kidnapping and beating death of a man in 1997.
The prison is about 32 km from the Canadian border, south of Quebec, and roadblocks were set up in the area, WIRY-AM reported.
The escape also prompted the Ontario Provincial Police force to issue an internal alert to its officers.
Due to the close proximity of the prison to the Canadian border, OPP officers are patrolling with "heightened vigilance," said Sgt. Peter Leon, the force's provincial media relations co-ordinator.
However, Leon stressed that there was no indication the two fugitives had crossed the border into Ontario, or were even headed that way. He said the primary purpose of the alert was to keep officers safe.
Maj. Charles E. Guess of the New York State police said more than 200 officers from multiple agencies were searching for the inmates. The search included bloodhounds and aerial surveillance, he said.
The two fugitive's adjoining cells were found empty during a morning check, said Anthony Annucci, the acting state corrections commissioner.
"A search revealed that there was a hole cut out of the back of the cell through which these inmates escaped," Annucci said. "They went onto a catwalk which is about six stories high. We estimate they climbed down and had power tools and were able to get out to this facility through tunnels, cutting away at several spots."
Authorities said there are many questions including how the men acquired the tools. Annucci said prison authorities are checking to see if any power tools are missing from contractors at the prison.
Cuomo said the prison break was the first escape from the maximum-security portion of the prison since it was built in 1865.
Sweat is white, 5 feet 11 inches, with brown hair and green eyes and weighs 165 pounds, police said. He has tattoos on his left bicep and his right fingers.
Matt is white, 6 feet tall, with black hair and hazel eyes, according to police. He weighs 210 pounds and has tattoos including "Mexico Forever" on his back, a heart on his chest and left shoulder and a Marine Corps insignia on his right shoulder.
Sweat and another man fired 15 rounds into Deputy Kevin Tarsia on the Fourth of July in 2002 shortly after using a pickup truck to break into a Pennsylvania woman's house, stealing rifles and handguns, authorities have said.
And nearly a decade after the 1997 kidnapping, murder and dismemberment of his former boss, William Rickerson, in upstate New York, Matt was returned to the U.S. from Mexico where he had fled to and been arrested for fatally stabbing another American outside a bar in a robbery attempt. He was convicted in 2008 of Rickerson's death.
With files from The Canadian Press