GMB, the general workers' union, has joined Unite and National Union of Rail, Maritime and Transport Workers (RMT) to call for Super Pumas to not be used for any commercial passenger flights to and from offshore oil and gas installations within Britain.
David Hulse, GMB National officer for workers in the offshore oil sector, said: "All Super Puma helicopter flights to UK installations must remain grounded while a full investigation is undertaken and conclusions drawn."
GMB also backed calls for an emergency debate in the Scottish Parliament over safety standards in the offshore sector.
Mr Hulse added: "The offshore employers have a duty of care to workers in the industry.
"Health and safety standards have failed miserably. The level of confidence the workforce has in the current standards is at an all-time low. "
Meanwhile, the RMT called for safety improvements as it staged a rally in Aberdeen five days after the Super Puma helicopter came down in the water off the southern tip of Shetland.
The crash, which claimed the lives of three men and one woman on Friday, was the fifth incident involving Super Pumas in the North Sea since 2009.
RMT general secretary Bob Crow attended a rally outside the union's Crown Street office.
"One thing's for sure, our members shouldn't pay the ultimate price of losing their life as a result of going to work," he said.
He said that while the investigation was still ongoing there was no way of knowing what caused the crash.
He said: "We've got to make sure that we learn from those investigations.
"Next week there might be a war in Syria and the Aberdeen issue will be off the media agenda and forgotten. We've got to make sure that the industry learns the lessons."
The Helicopter Safety Steering Group (HSSG) - made up of helicopter operators and users, trade unions and regulators - adjourned its meeting without reaching a decision on a review of the suspension of Super Puma flights.
The group will reconvene today at 1pm.
Aberdeen City Council has set up a support centre for people affected by the helicopter tragedy.