But, speaking to reporters this morning, Twyford said it was too soon to be talking about a review as there is still very little information available about the circumstances of the death.
"I think it would be premature to make any comment about the circumstances of this incident or any implications it might have for safety regulation until we know more about what exactly happened."
Twyford said his thoughts were with the family of the man who died.
The Government already has work underway on assessing the safety regulations of Lime and other such e-scooters, which is being led by Associate Transport Minister Julie Anne Genter.
"That will include rules about where Lime scooters can be used in terms of speed limits," Twyford said.
But he said it was too early to say if that work will be brought forward.
A Lime spokeswoman this morning said the company was "devastated to learn of this tragic incident in Auckland overnight, and our thoughts are with the victim's family and friends during this extremely difficult time".
She said the company had been in contact with local authorities and would continue to assist however possible.
Fletcher said when it comes to e-scooters, one death is too many and said tighter safety regulations were needed.
Auckland Mayor Phil Goff said like all accidents on our roads, this death was a tragedy and his thoughts were with the victim's family and friends.
"It is not sensible to speculate on the cause of the accident until the police advise of the circumstances.
"When the police and coroner reports are available, we will know if any other action needs to be taken by local or central government agencies," Goff said.
