“ We send our deepest condolences to the family at this difficult time,” the statement said.
Yahya Ibrahim, a Muslim Chaplain at Curtin University and the University of Western Australia, told RN Breakfast that funeral prayers had been held for the Australian, believed to be a man from Sydney.
“It is somebody who was elderly who sadly found his last moments seeking God,” he said.
“The environment is what it is and it is unfortunate that there was a heatwave in the peak of the Hajj.
“It happened all within a certain number of hours, really a peak after some of the hottest parts of the day and the week.”
Saudi Arabia has not commented on the death toll amid the heat during the pilgrimage.
Temperatures in high 40s recorded
Hundreds of people had lined up at the Emergency Complex in Al-Muaisem neighbourhood in Mecca, trying to get information about their missing family members.
Temperatures on Tuesday reached 47 degrees Celsius in Mecca and the sacred sites in and around the city, according to the Saudi National Center for Meteorology.
Mr Ibrahim said there were support services for people completing the Hajj but the extreme heat made it difficult to keep people safe.
“There are literally hundreds of thousands of people who are out there trying their best to try to make sure the literally millions of people converging on a very small swathe of land are looked after,” he said.
“But when temperatures reach beyond 50 … people are not willing to pay heed or think at times that they are not as overwhelmed as they are.”