The governor called the offer of $50,000 for each prisoner an unusual step for the state, but said "it is appropriate."
"These are dangerous men," Cuomo said, adding that they are "capable of committing grave crimes once again."
More than 150 leads have been developed so far, Major Charles Guess of the New York State Police said today, and Cuomo urged any New Yorkers with information to come forward.
"They could be anywhere across the state" or in neighboring states, Cuomo said.
Sweat, 34, is serving a life sentence after he was convicted of killing a Broome County sheriff's deputy in 2002. Matt, 48, is serving 25 years to life in prison after he kidnapped and beat a man to death in 1997.
"These are killers. They are murderers," Cuomo said. "There's never been a question about the crimes they committed. They are now on the loose, and our first order of business is apprehending them."
Earlier today, Cuomo told ABC News that what troubled him most about the escape was that the two men needed power tools to pull it off, and there was no way they could have done it in total secrecy.
"They had to be heard," he said.
The governor, who toured the prison Saturday, described the escaped convicts as "resourceful" and "dangerous."
"This was the first breakout since 1865 and I want to make sure that it's the last," Cuomo said.
The escapees left a note behind that read "have a nice day." Cuomo said he suspects it was their way of saying they were doing something that had never been done before.
"I'm sure they knew that since it was the first escape it was going to be a big deal," he said. "But we'll get them back and we'll give them the note back."