"Over the coming weeks we will review of all aspects of this tragic incident as well as our operating processes to ensure the mine is ready for a safe restart and continued safe operation," French said yesterday.
"Our thoughts remain with Ian's family, friends and colleagues impacted by the tragedy."
The Queensland Department of Natural Resources and Mines said Downes was fatally injured when part of an underground roadway wall struck him while he was pressure grouting it.
This followed a fatality at the mine in May this year when a worker was believed to have been asphyxiated by noxious gas.
Last week a union official told MiningNews.net sister publication International Coal News that Anglo should urgently review its workplace practices no matter what the new investigation brings.
"We remain 100% committed to eliminating fatalities within our business and will do all we can to deliver this objective," French said yesterday.
"We must learn from this event to ensure this never happens again. Our one and only focus right now is our people's safety and making sure that when we do restart we are totally confident the working environment is safe for all those who work at the Grasstree mine.
"In the meantime, we will work closely with the Queensland Mines Inspectorate and conduct our own investigation to learn from this tragic event and proactively take all actions we believe necessary to safeguard all the people who work at our Grasstree operation before we recommence operations."
Anglo has not yet determined when operations at Grasstree would resume.
Two senior mines inspectors and an investigator first visited the recent accident scene on Monday.