Police searching for the second of two escaped prisoners who pulled off an elaborate breakout from a maximum-security New York prison three weeks ago say that the remaining escapee is fatigued and likely to make a mistake after law enforcement officers shot and killed his accomplice Friday.

Hundreds of law enforcement officers have converged on a wooded area 30 miles from the Clinton Correctional Facility with helicopters and search dogs, where David Sweat is believed to be hiding. Sweat and fellow escapee Richard Matt escaped from the maximum-security prison in Dannemora about three weeks ago. 

Matt was shot Friday afternoon after an encounter with border patrol agents.

About 1,200 searchers focused intensely on 22 square miles Saturday encompassing thick forests and heavy brush around where Matt was killed.

Franklin County Sheriff Kevin Mulverhill told Fox News that police are very motivated after Friday's events, while Sweat is likely fatigued, increasing the chances he will slip up.

"He's been out of prison for three weeks. He's been on the run for three weeks," Mulverhill said. "He's in this area, he's now lost his cellmate, his escapemate is gone, he's alone."

"If he's in this perimeter, we're pushing him we're moving him around," Mulverhill said.  He's tired, he's going to make a mistake."

Sweat also could have an even tougher time now without someone to take turns resting with and watch his back, said Clinton County Sheriff David Favro.

"Now it's a one-man show and it makes it more difficult for him," Favro said. "And I'm sure fatigue is setting in for him as well, knowing the guy he was with has already been shot."

Authorities said Matt was shot by a border patrol agent when he failed to comply with orders in the woods near a cabin where a shot had been fired earlier in the day at a camping trailer. A 20-gauge shotgun was found on Matt, though he didn’t fire it at officers, authorities said.

"They verbally challenged him, told him to put up his hands. And at that time, he was shot when he didn't comply," New York State Police Superintendent Joseph D'Amico said at a news conference late Friday.

The breakthrough came Friday shortly before 2 p.m., when a person towing a camper head a loud sound and thought a tire had blown out. Finding the tire intact, the driver drove another eight miles before discovering a bullet hole.

Authorities converged on the location where the sound was heard and discovered the smell of gunfire inside a cabin. D’Amico said there was also evidence someone had fled out the back door.

A noise -- perhaps a cough -- ultimately did Matt in. A border patrol team discovered Matt, who was shot after failing to heed a command to raise his hands.

"As we were doing the ground search in the area, there was movement detected by officers on the ground, what they believed to be coughs. So they knew that they were dealing with humans as opposed to wildlife," he said.

"We have a lot of people in the area. We have canines and we have a decent perimeter set up and we're searching for Sweat at this time," he said.

The pair escaped the prison together on June 6. Gov. Andrew Cuomo called them “dangerous, dangerous men.”

Police blocked off all roads as officers hunted for Sweat in an area around Titusville Mountain State Forest in Malone, spanning 22 square miles.

Mitch Johnson said one of his best friends checked on his hunting cabin in Malone Friday afternoon and called police after noticing the scent of grape flavored gin as soon as he stepped into his cabin and spotting the bottle that had gone untouched for years resting on a kitchen table.

Johnson said his friend, correction officer Bob Willett, told him he summoned police about an hour before Matt was fatally shot and then heard a flurry of gun blasts.

Matt and Sweat used power tools to saw through a steel cell wall and several steel steam pipes, bashed a hole through a 2-foot-thick brick wall, and squirmed through pipes to escape.

Sweat was serving a sentence of life without parole in the killing of a sheriff's deputy in Broome County in 2002. Matt was serving 25 years to life for the killing and dismembering of his former boss.

A civilian worker at the prison has been charged with helping the killers flee by giving them hacksaw blades, chisels and other tools.

Prosecutors said Joyce Mitchell, a prison tailoring shop instructor who got close to the men while working with them, had agreed to be their getaway driver but backed out because she felt guilty for participating. Mitchell pleaded not guilty June 15 to charges including felony promoting prison contraband.

Authorities said the men had filled their beds in their adjacent cells with clothes to make it appear they were sleeping when guards made overnight rounds. On a cut steam pipe, the prisoners left a taunting note containing a crude caricature of an Asian face and the words "Have a nice day."

Clinton County District Attorney Andrew Wylie said they apparently used tools stored by prison contractors, taking care to return them to their toolboxes after each night's work.

On June 24, authorities charged Clinton correction officer Gene Palmer with promoting prison contraband, tampering with physical evidence and official misconduct. Officials said he gave the two prisoners the frozen hamburger meat Joyce Mitchell had used to hide the tools she smuggled to Sweat and Matt. Palmer's attorney said he had no knowledge that the meat contained hacksaw blades, a bit and a screwdriver.

Dannemora, built in 1845, occupies just over 1 square mile within the northern reaches of the Adirondack Forest Preserve and is surrounded by forest and farmland. The stark white perimeter wall of the prison, topped with guard towers, borders a main street in the village's business district.

The escape was the first in history from Clinton Correctional's maximum-security portion. In July 2003, two convicted murderers used tools from a carpentry shop at Elmira Correctional Facility to dig a hole in the roof of their cell and a rope of bedsheets to go over the wall. They were captured within three days, and a subsequent state investigation cited lax inmate supervision, poor tool control and incomplete cell searches.

The Associated Press and Fox News' Rick Leventhal contributed to this report