MILAN, Feb 7 (Reuters) - Three people died in an avalanche on Saturday while skiing off-piste in the Trentino-Alto Adige and Lombardy mountains, regions that include some Winter Olympic venues in Milan and Cortina, Italy's Alps rescue service said.

Two avalanches struck the Dolomite Mountains region near Cortina d'Ampezzo, where women's skiing competitions are held.

The rescue service said it recovered the body of a man who had been skiing off-piste with three other skiers at Punta Roca, a 3,300-meter peak on Mount Marmolada, the highest mountain in the Dolomites.

Two other skiers died off-piste in Albosagia, a village in the Valtellina Valley, about 65 kilometers east of Bormio, where all the men's skiing competitions are held.

The rescue service said it had not yet received confirmation of a possible fourth victim in Trentino-Alto Adige, where local media reported that a man injured in an earlier avalanche had died in hospital.

The heavy snowfall that has fallen on the Alps in recent days has caused several avalanches.

Earlier this week, another avalanche in the Trentino-Alto Adige region killed two Finnish skiers.