ZERMATT, Switzerland - Heavy snowfall has cut off many villages and resorts across the Alps, trapping about 13,000 tourists at Zermatt, one of Switzerland's most popular ski areas, officials said on Tuesday.

Helicopters spent two hours airlifting some of those stranded to nearby villages, while others remained stuck in the resort for a second day running after snow blocked road and rail links.

In the Pyrenees, a skier was killed and another injured after avalanches in Aragnouet on the slopes of Pique Poque mountain, according to local police.

In the French Alps, a slight break in the weather meant rescuers could begin looking for a British skier who went missing on Sunday in the resort of Tignes, police said.

"The people in charge are working with high pressure," a statement on Zermatt's official website said as tourists and locals bedded in for another night in the resort.

But an avalanche risk at its highest level means the stranded tourists will not be able to take advantage of the abundant snow for the time being.

"It is not possible to do downhill or cross country (skiing), but that's OK. It's a bit romantic," resort spokesperson Janine Imesch said, adding that "there is no panic".

The heavy snowfall also caused power outages in some other areas of the southern Swiss canton of Valais, and a number of other villages were also cut off, with the Simplon region of Valais hit by 2 meters of snow over 24 hours, the ATS news agency reported.

Mud and rockslides, as well as flooding, closed a number of roads across Valais. At lower altitudes, heavy rains forced the evacuation of around 20 people from Eyholz village with the nearby hamlet of Mottec also emptied as a precaution, Swiss media reports said.