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They said they had been notified of an “overdue” aircraft operated by the airline Bering Air at 16:00 local time on Thursday (01:00 GMT).
The 10 people on board comprised nine passengers and a pilot, the update from the Alaska Department of Public Safety said. There was no information immediately available about who was on board.
The volunteer fire department in the landing city Nome said the pilot had told air traffic controllers that “he intended to enter a holding pattern while waiting for the runway to be cleared”.
The BBC has contacted Bering Air for comment.
Giving information about its search and rescue mission, the coastguard said a plane had been sent to search for the last known positions of the missing craft.
The search plane – which includes specialised equipment to locate objects and people with no visible conditions – will fly in a grid pattern over the water and shoreline.
Elmendorf Air Force Base in Anchorage has also sent flight support.
