UPDATED 4.39pm: A foreign tramper has been waiting for nearly a month at a remote South Island hut to be saved after her partner was killed falling down a slope in the South Island.

Police say the female tramper from the Czech Republic has been holed up at a hut on the Routeburn Track area since late July after her partner died after falling down a steep slope.

Police and searchers went in to the area yesterday after being told the couple were overdue.

It was the Czech Consulate which raised concerns with the police yesterday about the pair.

Police first found the couple’s vehicle at the Routeburn Track carpark and then initiated a search and rescue operation, which included the use of a helicopter.

Rescuers searched huts and areas of high risk in avalanches, Jensen said.

They found the woman in a Department of Conservation warden's hut.

The woman advised Police the couple had entered the track on July 24 and her partner fell down a steep slope four days later.

Otago Lakes central area commander Inspector Olaf Jensen said the woman managed to reach him, however, it’s believed he died not long afterwards.

Police believed the man fell about 2km from the hut where the woman was staying. The woman spent a number of nights in the open after his death before arriving at the hut where she's been since early August

She didn’t go back to him after he died, Jensen said.

Inspector Jensen said the woman appeared to have suffered from minor frost bite. She was examined at hospital after being found yesterday but didn’t require treatment.

He said the woman made the right decision to stay at the hut.

“Some of the comments asking why she wasn’t found are unhelpful. No one had been through the area and because of her physical capability, she wasn’t able to walk out.

“Given her experience, and the avalanche risk, she made the decision to stay in the hut, and that was the right decision.”

The woman, who was in her late 20s or early 30s, made an “H” in the snow calling for help.

There was a radio in the hut, but she was unable to make it work, Jensen said.

Inspector Jensen described the woman’s ordeal as “traumatic”.

Her and her male partner, who was also in his late 20s or early 30s, had some tramping experience and were reasonably well-equipped but didn’t seem to have told many people they were doing the tramp, Jensen said.

Search and rescue was now involved in a recovery operation for the man, which Police hoped to finish by night time. His next of kin have been advised of his death.

Police are now trying to trace the movements of the pair before July 24.

Officers have been asking around some of the hotels, camping grounds and backpacking hostels if the couple had stayed with them.

Ultimate Hikes General Manager Noel Saxon said it's unusual for someone to be stuck in a hut for so long.

"I know that people do walk through there in the winter time, it's not unusual. It surprises me that someone hasn't come across her at some stage." 

Otago Tramping and Mountaineering Club president Richard Forbes said having the right safety equipment is vital.

"This woman was on her own in the hut for a month. It sounded like she never saw anybody else. If she had have had a beacon she could have set that off and help would have been there very quickly."

Some locals expressed surprise that the track was attempted in such wintry conditions.

But one local hunter believed that, despite recent snow dumps, it would've possible to walk out and raise the alarm.

"It's all very strange," the hunter said.

Wakatipu Tramping club secretary Lindsay Jackson said the track is very different in the winter, and should only be considered by those with alpine experience.

She said she has no idea how the woman could have survived for a whole month, who probably only had a few days food.

Police and SAR will be returning to the track this afternoon in an effort to locate her companion, conditions permitting.

Police are refusing to do media interviews until at least this afternoon - they say they need to interview the woman first.

DOC said it's supporting the young Czech national.

In a statement, DOC's Wakatipu operations manager Geoff Owen has labelled the situation as a tragic accident, and said they're offering their sympathies to the families involved.

He said reduced facilities, avalanche risks and weather conditions present a number of hazards during the off-season.

DOC is also encouraging people to let others know what their plans are before heading outdoors.