Relatives, police, Waiouru army personnel, local iwi and more than 100 Land Search and Rescue volunteers have conducted extensive searches over the past eight days, coming from as far afield as Auckland and Wellington.
The discovery of a water bottle, shoes and a beanie thought to belong to one of the men has not yet led to their rescue, but Inspector Tony Jeurissen said police continued to have hope.
"As a result of everyone's relentless focus, we continue to find items of interest," he said.
"These small developments keep everyone going each day."
Taurima's father, Tony Taurima, said that his whanau was "devastated" by his disappearance.
"I just want him out of there, that's all I want, I don't care what it takes," he told Newshub.
"He's still a kid in my eyes. He's still my boy."
The weather has been wet and cold in the area for the past week, and a severe weather watch has now been issued for the lower North Island, with snow forecast overnight on the Desert Rd.
Family members say neither man is equipped for survival in the bush.