The cross-country skiers, five of them members of the same family from Valais canton, went missing near the 3,710 metre-high Tête Blanche mountain on Saturday on the Zermatt-Arolla path.

Authorities have not given the cause of death for the five found late on Sunday but described "catastrophic" conditions with snow storms, high winds and extreme temperatures.

"Our priority is to find that sixth person," Christian Varone, cantonal police chief, told journalists.

"As long as there is hope we will do all we can, but we have to be realistic about the conditions that person has lived through over the past 48 hours."

Mountain guide Anjan Truffer told Swiss broadcaster SRF that two of the bodies had to be dug out from beneath the snow.

"The end result was clear, the people froze to death. They got caught in a storm, probably lost their bearings and didn't know what to do." He said that rescuers advised them to dig a snow cave after one of them sounded the alarm.

"You could see that they tried, but unfortunately they were very poorly equipped and with those little shovels in the hard snow, there wasn't much they could do."

THWARTED RESCUE ATTEMPT

The incident is one of the most deadly in the Swiss Alps in recent years.

Eleven helicopters were part of a search and rescue operation over the weekend as well as a five-person team that left Zermatt on foot to reach the area near the Matterhorn, which straddles the border between Switzerland and Italy.

But the search party had to turn back late on Saturday within 500 metres (yards) of the group's last reported altitude.

"Everything was done in terms of personnel and means and everybody worked 24 hours a day to try to achieve the impossible. But we have to bow to nature," said Varone.

Police said the group of skiers included people between the ages of 21 and 58. A formal investigation is under way.

Authorities urged extreme caution given ongoing risks of avalanches which also killed another off-piste skier in the same canton at the weekend.

(Reporting by Emma Farge; Additional reporting by Dave Graham in Zurich; Editing by Lucy Marks and Christina Fincher)

By Emma Farge