They say the search for Prabhdeep Srawn in the Kosciuszko National Park involved nine police officers and National Parks and Wildlife Service personnel, but the operation was hampered by bad weather.
New South Wales Police have been steadily scaling back the search for Srawn after failing to find any trace of the 25-year-old Brampton, Ont., man who has been missing since May 13.
On Tuesday, they hinted that the search would last only a couple more days.
A police spokesman told The Canadian Press early Friday that his understanding was that the search would continue for a few more days but that local police would make the decision based on available resources.
Srawn's family has said it will continue the rescue effort when the official search ends.
Diane Ablonczy, the minister of state for consular affairs, met with the family Thursday and indicated that she had spoken with both Australia's foreign minister and High Commissioner to Canada.
"We understand that the Australians must make their own decisions about their resources, but we will continue to engage the Australian government on the family's behalf," said Joshua Zanin, a spokesman for the minister.
Srawn is a Canadian army reservist and his family and supporters still believe he will be found alive because he has had extensive survivor training and hiking experience.
Both NDP Leader Thomas Mulcair and Liberal Leader Justin Trudeau have appealed to the federal government to encourage Australian authorities to continue looking for Srawn.
"Prabhdeep Srawn has selflessly served this country and must not be abandoned during this time of great need, "Mulcair wrote to Prime Minister Stephen Harper on Tuesday.
In his earlier letter to Foreign Affairs Minister John Baird, Trudeau said he joins Srawn's family in urging Canada's "continued support of the ongoing rescue efforts."