Flights were suspended after an AS332 L2 Super Puma crashed as it approached Sumburgh airport on the southern tip of Shetland, killing three men and one woman.
Step Change in Safety's Helicopter Safety Steering Group (HSSG) said the fleet should return to the skies after a two-day meeting in Aberdeen to review the suspension.
But a union representing oil industry workers condemned the decision. The L2 Super Puma model of helicopter involved in the tragedy is to stay grounded.
Unite Scottish Secretary Pat Rafferty said: "The continued grounding of the L2 fleet - the same type involved in last Friday's crash resulting in four fatalities and also in the April 2009 crash with 16 fatalities - is the bare minimum that the industry can do until the recovered black box's data fully establishes why this tragedy occurred.
"The decision of the HSSG to return the Super Puma L type, L1 type and the EC225 type, as per its original service plan, to UK offshore operations should be approached with caution and sensitivity.
"Confidence has been shattered and the industry needs to provide substantive evidence - not opinion - to its workers demonstrating the airworthiness of the helicopters that are now returning to operations.
He said the union is demanding guarantees from employers that workers who feel unable to fly will not be subject to pressure or the threat of dismissal.
Mr Rafferty added that the industry cannot simply expect the workfore to "get their boots on and get back to work."
In a statement, the HSSG said; "The 'time out for safety' has been completed and there is no evidence to support a continuation of the temporary suspension of the entire Super Puma fleet.
"As a consequence, the HSSG supports the return to active service of all variants of the Super Puma fleet."
CHC had temporarily suspended all flights of the three types of Super Puma helicopter that it operates - the L, L2 and EC225.
Fellow operators Bond Offshore Helicopters and Bristow also enforced a temporary suspension of all Super Puma flights except emergency rescue missions.
The Super Puma is said to make up about half of the UK offshore industry's 75-strong helicopter fleet and the freeze has caused disruption to the movement of workers on and offshore.
Les Linklater, Step Change in Safety's team leader, said that there were almost 16,000 people offshore, with more than 12,000 in the areas most affected by the suspension - the central and northern North Sea.
"Today, there are over 250 people who have spent more than 21 days offshore, this is increasing daily and they and their families are wondering when they are going to get home," he said.
"Industry has a duty of care to all offshore workers both in terms of their safety and their well-being; we must consider the cumulative risk of the 'time out'.
"We must avoid a further tragedy through the introduction of human factor-based risk such as fatigue, stress and other well-being concerns that increase the likelihood of a high consequence-low frequency event.
"By taking the time out for safety over the weekend, we have had the opportunity to review key elements of our fleet and better understand the positions of the authorities that determine the airworthiness and operational compliance and safety of our helicopter fleet."
Helicopter operators are satisfied there is no reason to believe there is an inherent mechanical problem with any of the Super Puma models, the HSSG said.
Sarah Darnley, 45, of Elgin, Duncan Munro, 46, from Bishop Auckland, Gary McCrossan, 59, from Inverness, and George Allison, 57, from Winchester died in the crash.