Gov. Andrew Cuomo said they may have crossed into Canada or left for another state or could even have headed toward Mexico.
Canada Border Services Agency on the weekend sent a "look out" on the escape to its officers and said Monday it continued to exercise its usual vigilance.
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.
The governor said Monday that investigators are looking into whether civilian employees or private contractors helped the men obtain the power tools. Cuomo said during appearances on television morning news shows that he'd be "shocked" if a prison guard was involved in the escape.
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, just over 30 kilometres south of the Canadian border.
It was the first escape from the maximum-security portion of the prison, which was built in 1845.
A spokeswoman with the Canada Border Services Agency said Monday there was no update on the status of the escapees. On Sunday, the border agency sent out a "look-out" to all of its officers about the escaped convicts.
"We continue to exercise our usual vigilance and bring more attention to the possibility that these individuals show at our designated ports of entry," said border agency spokeswoman Jacqueline Roby on Monday morning.
Quebec's provincial police, the Surete du Quebec, said they are not involved in the manhunt, but are on standby should the RCMP ask for help.
The RCMP said on the weekend it advised its officers in detachments close to the border to be on the lookout for the two escaped fugitives, but there was ``no manhunt'' since the RCMP had received no information indicating the two fugitives crossed the border.
The escape prompted the Ontario Provincial Police to issue an internal alert to its officers on the weekend, with officers patrolling with "heightened vigilance." OPP said the primary purpose of the alert was to keep officers safe.
Prison officials found the inmates' beds inside the 170-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.
The men may have had assistance outside the prison, perhaps meeting up with someone who helped them leave the area, investigators said.
Cuomo said the men even could have fled toward Mexico, where Matt served time for killing a man in 1998.
The governor 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.
Martin Horn, former commissioner of the New York City Department of Correction and a professor at the John Jay College of Criminal Justice, said the prison maintains an inventory of tools — "every pair of scissors, every wrench, every power tool."
He said many questions remain, among them how long it took to prepare for the escape, why no one heard the noise and how the prisoners hid the holes they made.
"Clinton is as secure a prison as you'll find anywhere in the United States," said Horn. "If it can happen at Clinton, it can happen anywhere."
Associated Press Writer Verena Dobnik contributed to this report.
With files from The Canadian Press