RCMP and Iglulik Search and Rescue have been looking for the two men since Dec. 2 when their snowmobile went into Hooper Inlet.
Police on Friday released the names of the missing men: Roger Ulluliyarnat, 28; and Jose Kangok, 24.
Mayor Elijah Evaloarjuk said that so far nothing has been recovered.
The underwater search has been called off. Emergency Medical Operations have been using an underwater camera to search for evidence of the missing men.
Eric Doig, who provided the camera, says the camera was used to its maximum, covering the immediate area where the men were last seen.
Evaloarjuk said the entire community has been affected by the news of the incident.
"On Tuesday everyone was waiting for any news from the search party," he said. "Our sympathies are going out to the family of the two young men."
The men were brothers-in-law travelling in a group of four to Hall Beach from Iglulik on three snowmobiles.
Two snowmobiles plunged into open water in Hooper Inlet and the two men were pulled under with their machine.
One man managed to swim to solid ice. He was picked up by the third snowmobile.
The two survivors returned to Iglulik to report the accident.
"It looked like the sleds were travelling really fast when they hit open water," said Evaloarjuk
Family found safe after search
It was the second incident that happened between Hall Beach and Iglulik in the same week.
On Monday night a family, travelling from Hall Beach to Iglulik was reported missing when they didn't arrive on time.
The family was left stranded between the two communities when their snowmobile ran out of gas.
Evaloarjuk said the family was well prepared to spend some time on the land. They were picked up by a search team and taken to Iglulik.