MINNEAPOLIS — The tiny bodies of two young brothers who disappeared while playing outside their home on the Red Lake Indian Reservation were found encased in ice in nearby First Thunders Lake, four months after the search for them began.

“Our worst fears were confirmed,” FBI Special Agent Ralph Boelter said, announcing that the boys had been found about a halfmile from their home.

Police dogs picked up the scent of Tristan Anthony White, 4, and Avery Lee Stately, 2, on Sunday, the first day of organized searching after the weather warmed, Mr. Boelter said.

The two boys, both American Indian, disappeared November 22 from their home in a remote area near the Canadian border. Authorities have not determined whether they somehow wandered out onto the lake’s thin ice and fell in or if foul play was involved in their deaths.

They might have been trying to reach a beaver dam, which was near where the bodies were found, Mr. Boelter said.

Divers had searched First Thunders Lake shortly after the two were reported missing, and hundreds of volunteers and law enforcement officers scoured the area, but they found no sign of the boys. The initial ground search was called off after five days. Mr. Boelter said search teams resumed their work on Sunday with the warmer weather.

“There’s a lot of mud and weeds down there,” Tribal Chairman Floyd [Buck] Jourdain Jr. told the Star-Tribune. “So, it’s not unimaginable that they would sink, get entangled, or stuck in the mud.”

“So many people were hoping for a safe return back to their family,” Mr. Jourdain said.

The boys’ mother, Alicia White, and Avery’s father, Jeff Stately, had feared the children were abducted.