Searchers made voice contact with the missing pair yesterday afternoon, but only for a short time. The men then went silent, making it impossible to find them, police said.
Today search teams found some clothes and evidence of a recent fire, but nothing else has been found since.
The search will go on until it is too dark to continue, police said.
Weather conditions meant a helicopter could not be deployed to help search for the men.
"The longer these young men are out there, ill-prepared in a bush environment with adverse weather conditions, the less likely it is there will be a successful outcome," Bay of Plenty operations manager Inspector Kevin Taylor said.
The two men are believed to be the same two who fled police in a stolen car on Saturday.
Police attempted to stop the stolen car about 3pm before the driver fled at speed north on the Desert Rd, Taylor said.
The car was eventually abandoned on a track off Tree Trunk Gorge Rd, off the Desert Rd, near the Three Sisters bends.
The driver and passenger had run off into the bush.
Taylor said police tried to find them but they actively avoided officers and were not found.
The incident prompted police to warn all road users to report sightings of pedestrians or hitchhikers in the area.
On Sunday morning based on information provided by family members and a subsequent 111 call from one of the offenders, it was clear the two had become lost in the bush, Taylor said.
The focus then changed to a search and rescue operation to remove the two men from the dangerous situation they were now in.
As one of the callers only had 2 per cent phone battery left at the time they called, police have only been able to obtain minimal details on their whereabouts.
Police from the Bay of Plenty district and a helicopter searched the area until 11pm last night but they were not found.
Taylor said police were now seriously concerned for their welfare considering their lack of experience in the bush and inappropriate clothing they had on them.
He said conditions overnight had been very cold and wet and it was likely both would now be suffering from hypothermia.
"These people are not trampers or hunters and are not prepared for the bush ... The longer it goes on, the less hopeful we are, to be honest," Taylor said.
