The Eurocopter Super Puma helicopter ditched into the sea about two miles from Sumburgh airport in Shetland on Friday night. It was carrying 16 passengers and two crew members.
The aircraft's operator CHC, a company that serves offshore oil and gas platforms, said the aircraft was approaching the airport when it lost contact with air traffic control. The coastguard agency said it sent helicopters and lifeboats to the scene after receiving a distress signal.
"There appears to have been a catastrophic loss of power which meant the helicopter suddenly dropped into the sea without any opportunity to make a controlled landing," said Jim Nicholson, a rescue coordinator.
CHC would not speculate on what caused the crash, saying it would cooperate fully with an investigation by police and the British Air Accidents Investigation Branch.
Police in Scotland said three bodies had been recovered, and they were searching for the fourth victim.
The 14 survivors were taken to a hospital, but their injuries were not serious. Oil company Total UK said one of them was its employee, while the others worked for separate contractor groups.
Friday's crash was the latest in a string of incidents involving Super Puma helicopters in Scotland in recent years. Two such helicopters ditched in the North Sea last year, with all the passengers rescued. One crashed while returning from a BP platform in 2009, killing 16 people.
Bob Crow, general secretary of the offshore workers' union RMT, said the Super Puma fleet should be grounded until the causes of Friday's crash were established.