First Minister Alex Salmond has said the Scottish Government should handle North Sea offshore safety.
He was speaking as an investigation got under way into the cause of a major fire that broke out on a platform.
More than 100 workers were evacuated from the Thistle Alpha platform after Sunday's fire but no-one was hurt.
The Health and Safety Executive (HSE) said its inspectors would visit the site, 120 miles north east of Shetland, as soon as weather conditions allowed.
Healthy and safety is not a devolved issue.
Mr Salmond said: "I think the Scottish Government should be responsible for all matters affecting the Scottish people, and that includes the waters around Scotland.
"I'm quite sure our colleagues in London have the same objectives and ambition. But I think closer management of the situation would benefit the industry, would benefit Scotland, and would benefit the workers in the North Sea.
"As recent events have shown, the oil and gas industry can be a dangerous one."
The HSE warned last week that safety on offshore oil and gas installations must be improved.
But it is understood the HSE found no serious problems when it inspected Thistle Alpha in May and again earlier this month.
A spokesman for Petrofac, which operates Thistle Alpha for the Swedish company Lundin Petroleum, said it was carrying out its own investigation into the fire.
The Unite union, which represents workers in the offshore oil industry, said it would co-operate with the inquiry and with looking at evacuation procedures.
The blaze took hold in the turbine module of the remote platform shortly after 0800 GMT on Sunday and smoke and flames billowed up from at least three levels.
Seven helicopters, including two from Norway, and an RAF Nimrod were called in to help.
Some 116 of the 159 people on board were airlifted to safety on two neighbouring oil platforms, Petrofac said.
The fire was put out by 1045 GMT and the rescue operation was scaled down.
Jake Molloy of the OILC union said the fixed firefighting systems on the platform were having difficulty coping with the blaze.
"Normally on a platform you have fixed systems which prevent the need to put people in to fight fires," he said.
"Those systems should be able to cope. It would appear that wasn't happening."
Thistle Alpha is more than 30 years old but Alan Curran, managing director of Lundin Britain, said age was not a factor.
He added: "Of course, the investigation that we conduct over the next few days will get to the root cause of the incident but I do believe that the age of the platform had absolutely nothing to do with the situation."
John Methven, director of health and safety for Petrofac, said the oil installation manager reacted correctly to events onboard.
He said: "The Thistle platform is perfectly safe, the emergency systems are all still working and we would not have upmanned the platform if that had not been the case.
"All our people are safe. There was nobody injured. Our emergency systems worked very well.
"We have a situation where initially the manager took a decision based on what he thought he saw at that time, which was perfectly correct, and now we are downscaling that whole incident significantly."
An HSE report released earlier this month said maintenance of many appliances in the North Sea was not being given enough attention.
Almost 100 North Sea installations were targeted in the three-year HSE inspection.
In more than half of the platforms the overall state of the plant was found to be poor.