Confidence among oil and gas workers is "so low" following the latest Super Puma crash that such an inquiry is needed, Mr Gray said.
The Scottish Government should "send an important signal" and back calls for a public inquiry, similar to that carried out by Lord Cullen in the wake of the Piper Alpha disaster 25 years ago, he said.
Mr Gray pressed Finance Secretary John Swinney on the issue as the minister gave a statement to Holyrood in the wake of the latest accident which saw three men and and one woman killed when a helicopter carrying workers from an offshore vessel crashed into the sea as it approached Shetland last Friday.
Fourteen people survived, including two crew.
Flights to and from offshore platforms have resumed following a temporary suspension, as experts said they found no information to suggest that a technical problem was to blame for the crash.
Mr Swinney stressed that "rebuilding the confidence of the men and women who travel to and from our offshore installations must be a key priority".
In April 2009 the same Super Puma model went down north-east of Peterhead on its return from a platform, killing all 14 passengers and two crew on board.
Mr Gray, Labour's finance and employment spokesman, said that in such circumstances a "wide-ranging, comprehensive and independent inquiry" is needed to restore workers' confidence in the transport.
"It is vital to restore confidence in helicopter transport for the sake of the industry but, above all, for the sake of the workforce and their families.
"However, this is the fifth incident in recent times when helicopters have ditched, with 20 lives lost in two of those accidents.
"Whatever the conclusions of the air accident investigation regarding the cause of the August 23 ditching, the truth is there are wider questions now being asked to which the workforce will need answers to their strongest satisfaction if confidence is to be regained. Indeed, confidence is now so low that an industry review will not likely be able to restore it.
"Only a wide-ranging, comprehensive and independent inquiry, like Lord Cullen's, will be able to do that, whatever the cause of the latest incident turns out to be."
He urged Mr Swinney to back this call, saying: "Beginning to rebuild confidence now, in our view, needs an early commitment. So will the Cabinet Secretary reconsider his position on this and send that important signal by supporting such an independent inquiry now."
Mr Swinney insisted that the "correct approach" is to wait for the findings from the Air Accidents Investigation Branch before deciding if a public inquiry is necessary.
"There is a set of steps that have to be taken properly and fully to address the circumstances of this incident," he told MSPs at Holyrood.
"There has to be an investigation of this particular incident, properly and fully, by the Air Accidents Investigation Branch (AAIB) and that has to report. And as a consequence of that, it is incumbent - because this is what the law says - that the Civil Aviation Authority has to consider and apply any relevant changes to the safety regime as a consequence of the investigation carried out by the AAIB.
"The Government maintains the correct approach is to wait for the sequence of investigations to be undertaken before we come to any conclusion about the need for a wider inquiry."
Because many of the issues raised by such an inquiry are reserved to Westminster, the UK Government would also need to agree to this, Mr Swinney also said.
"We will consider any further inquiries that are required once the conclusions of the AAIB investigation are to hand."
Tory MSP Alex Johnston, who repesents the North East region, backed the Finance Secretary's approach.
"I believe he is correct in saying calls for a public inquiry are premature. The Air Accidents Investigation Branch is the correct facility for the initial inquiry," he said.