Rescue teams hold "very grave" concerns for two men, possibly suffering hypothermia, after they were believed to have fled from police into inhospitable bush in the central North Island.

The men, aged in their 20s, abandoned a stolen car near the Desert Road before legging it into bushland in the Tongariro National Park on Saturday, police say.

But they are not equipped for the cold weather and during a 111 call with emergency teams on Sunday, the men reported being cold and numb.

Since then, they have not made contact with authorities but searchers on Monday afternoon located a campfire, a shoe and two piles of clothing before a shirt and matching shoe were found separately.

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Bay of Plenty operations manager Inspector Kevin Taylor says the discovery of discarded clothing is alarming.

"That's consistent with them being hypothermic," he said.

Hypothermic people sometimes experienced euphoria or delirium in which they take their clothes off despite this being the worst thing they can do.

On Tuesday, 40 volunteers from as far away as Tauranga and Whanganui were searching for the men, Taylor said.

Bad weather is preventing a helicopter from assisting the search, which will focus on the area radiating out from where the campfire and clothing was found.

"The bush is exceptionally dense and this is a challenging search," Taylor said.

"If the two individuals are in a condition where they're not responsive, they will only be found once a searcher is in their immediate vicinity.

"The longer these young men remain in these conditions, the less likely it is that they will survive.

"However, today we still remain determined and hopeful that we will find them alive."

- NZN