“The police reacted to it immediately,” Shaun Gillilland, the town supervisor in Willsboro, said, though he added that officials had not yet confirmed that the two men were the escaped prisoners.

Neighbors said they believed the two men had fled into the woods, which grow in thick nests amid rolling field. George Sayward, a farmer with about 300 acres of land off Middle Road, said law enforcement officers had arrived at his property around dawn and subsequently conducted a search across his land, moving closely together to the west, across railroad tracks that run roughly parallel to the lake.

The search area also included soggy lowlands — populated by geese, cows and tractors — and pocked by ponds, puddles and ruts. “It’s not going to be an easy walk, I’ll tell you that,” Mr. Sayward said. Still, by midafternoon, Capt. John H. Tibbetts of the New York State Police confirmed that the area near the potential sighting was being “flooded with police,” and residents hoped that the hunt for Mr. Matt and Mr. Sweat might be coming to an end.

Roads were closed, and corrections officers in body armor and armed with high-power rifles lined a country highway, while others kept watch with binoculars and peered through weapon scopes. One armed officer was seen in full jungle camouflage, and black armored vehicles were stationed on roads. Officers moved slowly across fields and entered empty buildings and barns en masse with guns drawn, again and again, before shouting, “Clear.”