The calls came as hopes briefly rose Wednesday of finding Prabhdeep Srawn when "voices" were heard in the search area in the Kosciuszko National Park.
But reports from the site in New South Wales say that poor weather is restricting search teams to the ground.
The 25-year-old Brampton, Ont., man hasn't been heard from since parking his rental car May 13 in a village near the park.
The Canberra Times reported Thursday that Srawn's family is frustrated that there is a lack of manpower but accepts that the authorities know what they are doing.
Meanwhile, friends of the family took to social media, urging the Australian military to join the search.
"We need military assistance to further search efforts and save Prabh Srawn who's been missing for 10 days," one wrote in a message addressed to Australian Prime Minister Julia Gillard.
"Please send in the army to help find Prabh Srawn. Rescuers are in need of assistance," another tweeted.
By early Thursday, nearly 3,000 people had joined a Facebook page dedicated to finding the law student.
Brampton Mayor Susan Fennell said in a message posted on the page that she had sent a letter to Prime Minister Stephen Harper, seeking additional support.
"Help find Prabh Srawn... he is a Bramptonian," Fennell wrote.
The family believes Srawn's chances of survival are a bit higher than a normal hiker because he has had extensive survival training as a reservist in both the Canadian and Australian military.
His cousin Tej Sahota told the Times that Srawn had extensive cold-weather camping experience from the Canadian army and may have taken shelter in areas of bush or a gully.