Mining giant Rio Tinto has had another crack at an apology over its destruction of ancient rock shelters in Western Australia after being embarrassed by a leaked recording of an internal meeting where staff raised concerns about the company's response to the incident.

Rio Tinto iron ore chief executive Chris Salisbury said in a statement issued late on Monday that he had been speaking directly with the Puutu Kunti Kurrama and Pinikura traditional owners and the company "unreservedly apologises for what happened at Juukan Gorge".