"Whilst other companies may continue to operate, a decision to resume our operations will be made later today when we have had time to complete a detailed analysis of yesterday's events as well as our systems and procedures," said Southern Lakes Heliski director Julian Field.
"We remain committed to aiding the external investigation team and have confidence that they will be able to determine the exact cause of this tragic accident."
While heli-skiing was not considered to be dangerous, Mr Field said that like any adventure activity, it carried "inherent risk".
"We take our responsibilities very seriously which is reflected in the fact that this is the first incident of this kind for our company and its predecessors in over 30 years of operations," he said.
"Our thoughts remain with the family and friends of the deceased."
Although Mr Greville was initially pulled from the avalanche debris, he died shortly after.
Police said the cause of death was still unknown, and had been referred to the coroner.
A post-mortem examination was scheduled for this morning.
Local police staff had been working closely with the Australian Embassy, and a number of Mr Greville's family were due to arrive today. The family has asked for privacy.
One of Southern Lakes Heliski's pilots called the company's operations team at 2.38pm to say that a group of skiers had been involved in an avalanche on the Hector Mountains.
It was confirmed one skier had been buried in snow, and emergency response procedures were activated immediately.
At 2.48pm, the company received confirmation that the skier had been located.
However, despite the efforts of guides and paramedics Mr Greville was pronounced dead at the scene.
Alpine Cliff Rescue team co-leader Chris Prudden last night said there had been new snow in the area, so there would be a few spots that were "a little bit sensitive".
Overall, however, the snow pack was relatively stable.
Two people in the last week had been dragged down by avalanches near the Remarkables and had been assisted by ski patrol.
"It's a signal to everyone you've got to be continuously vigilant on snow conditions.
"It doesn't matter even if the avalanche advisory report says the hazard is low, you've still got to be vigilant.
"There is no such thing as no avalanche danger when you're dealing with snow."
Mr Prudden said activities in the outdoors near Queenstown did involve risk.
"There is a statistic that goes with people going out in the back country.
"That could with heli-skiing, that could be on foot, ski touring, as people do, there's an element of risk all the time."
He said people did, however, need to take more care. and make themselves aware of safe practices.
Regional avalanche forecaster Chris Cochrane said there had been strong southerly winds in the last 24 hours which had caused "wind slab" conditions, where there was very stiff snow, causing tension in the snow pack.
In his bulletin yesterday he had said the weight of a single person could be enough to trigger an event.
"It's just an inherent danger that is always present in the back country."
- Additional reporting: Otago Daily Times