That minister is Iain Lees-Galloway. MBIE reports to 12 ministers including him.
Collins said any law changes would need to be passed by Parliament and regulation changes agreed to by Cabinet, following consultation.
MBIE officials would be among those responding to Prime Minister Jacinda Ardern's request for information on whether there are any investigation gaps that fall outside the current coronial inquiry being carried out by police and an investigation by WorkSafe.
Collins said adventure activities were "a diverse category, so the regulations focus on systems and processes operators need to manage the risks of the activity they are offering, rather than prescribe requirements according to specific risks".
She said MBIE had a team focused on workplace health and safety policy, which included the adventure activity regulations.
A new adventure activity regulatory regime was created in 2011, and was brought fully into force by 2014. The regulations were updated in 2016 to ensure they aligned with new Health and Safety at Work 2015 legislation.
Meanwhile, WorkSafe said 10 investigators were working in Whakatāne, the Bay of Plenty town closest to White Island from which tours to the volcano departed.
Another 10 Wellington-based WorkSafe staff were working on the investigation, a spokeswoman said. Three lawyers were advising.
The probe is the health and safety watchdog's biggest since it was formed in 2013.
WorkSafe would not comment on exactly what was being investigated, or how many, and what, White Island tourist operators were involved.
WorkSafe has 12 months from the date an incident is reported to it in which to file charges if a prosecution is to be pursued.
White Island is privately owned by Auckland's Buttle family. Only permitted operators were allowed to take tourists on guided visits to the island.
White Island Tours was one of the main operators out of Whakatāne. The company was the only operator registered under the regulations and was regularly audited, as recently as in the past few months. It was last year named New Zealand's safest place to work in a workplace safety award. One of two people still missing, presumed dead, is a White Island Tours guide.
At least three helicopter operators regularly took visitors to White Island.
Opposition leader Simon Bridges has said an independent investigation into the tragedy is inevitable and necessary to answers the questions of New Zealanders and overseas tourists.
Prime Minister Ardern this week stopped short of announcing a Government probe into the eruption, saying officials would be providing advice on the issue after the summer break.
Ardern said any probe would only fill gaps between two investigations already currently being carried out by WorkSafe and the coroner.
Bridges said the PM was being "unduly reticent".
"There will inevitably be those questions about whether tourists should have been on that island at this time, what the future of that tourism looks like, whether the recovery was done well," Bridges said.
"These are the sort of things New Zealanders and the international community will want to see there has been an independent inquiry on."
Bridges said it was also important to have a probe that was free of government departments.
A review in 2010 by the then Labour Department of risk management and safety in the adventure and outdoor commercial sectors concluded there were gaps in the safety management framework which allowed businesses to operate at different standards "than those generally accepted".
"While these gaps remain there is insufficient assurance that preventable accidents will not occur. This situation could result in harm to individuals and their families and damage to New Zealand's reputation as an international visitor destination."
However, the review report said there did not appear to be a fundamental problem in the sector's ability to develop appropriate safety systems.
The review was sparked by concerns about a number of serious incidents in the sector.
