"Our sympathies are with the family and particularly the man's wife who was also walking the track," Mr Saxon added.
He said the track was well-used and although there was some cloud, there was good visibility and no reports of heavy rain or other wild weather conditions at the time of the accident.
Mr Saxon said all trampers on Ultimate Hikes Guided Walks on Milford Track were safe.
The police Southern District Command Centre (DCC) confirmed the man died yesterday and it was understood he had sustained head injuries.
A rescue helicopter was sent to the area with a medic and winch operator. The helicopter then took the man's body to Te Anau.