Bob Crow of the RMT has accused employers of playing fast and loose with oil workers' lives by not suspending flights to allow full safety checks to take place.
It comes after the crash which led to the deaths of 16 men was found to have been caused by "catastrophic" gearbox failure.
The British Airline Pilots' Association (Balpa) has also raised concerns that safety is being jeopardised for the sake of commercial pressures.
The investigation found the gearbox had suffered a "major failure", which was not yet fully understood, leading the main rotor blades to break off and hit the helicopter.
The report by the Air Accidents Investigation Branch (AAIB) said the aircraft's manufacturer, Eurocopter, should carry out "additional inspections and enhanced monitoring" on its AS332 L2 models of Super Puma helicopters.
It also recommended that the European Aviation Safety Agency evaluates these checks and, when satisfied, makes them compulsory. Crow said he wanted all similar Super Pumas kept on the tarmac until they got the all-clear.
He said: "Our position is pretty clear: they should be grounded for a full inspection to take place before our members are absolutely satisfied that those Super Pumas are OK to fly.
"We're saying to our members: 'If you don't feel safe about going into those Puma helicopters then you should refuse to work on the grounds of health and safety.'"
Balpa general secretary Jim McAuslan wanted the investigation into the crash to look at wider issues about safety within the industry.
"Something is giving. The commercial pressures are making safety give a bit."
Chris Allen, health and safety director for Oil & Gas UK, the leading representative body for the UK offshore oil and gas industry, said: "Oil & Gas UK can confirm that helicopter companies operating flights to UK offshore installations today (Saturday] have carried out the additional checks that were required in the alert service bulletin issued by the manufacturer, Eurocopter, last night (Friday].
"The bulletin, which was made mandatory by the European Aviation Safety Agency, requires daily checks to be carried out on the Super Puma L2 and EC 225 to verify the condition of the main gearbox.
"The industry is committed to implementing all the recommendations which have so far been made by the AAIB and any others which emerge from the continuing investigation. The UK leads the world in the safety of offshore helicopter operations and we will do everything within our power to maintain and improve that position in order to protect the safety of our people."
A Scottish Government spokesman said: "It is vital that the cause of the crash is established so lessons can be learned and these types of tragedies can be avoided in future."
The 14 passengers and two crew who died were returning from BP's Miller platform when the helicopter crashed in the sea, 14 miles off the coast of Aberdeenshire.
The bodies of the victims have all been recovered and identified. Eight came from the north-east of Scotland, seven from the rest of the UK, and one from Latvia.
A memorial service for those who died is to be held on Wednesday in Aberdeen.