Regional police said two local women, aged 34 and 38, had been found dead, while four others, including a 44-year-old Italian man, had been injured and taken to hospital after the building collapsed.
There were reportedly eight people living in the three-story residential building in Davesco-Soragno, near Lugano, which Ticino police said was hit by a landslide just before 2:30 am (local time).
Another resident had returned home after the landslide hit and was unharmed, but police said they were still searching the area to make sure no one else was under the rubble.
Municipal and regional police were being helped in the mission by the fire brigade, civil protection units and a special search dog unit, police said.
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After weeks of heavy rain, southern Ticino has been hit by severe flooding, which worsened after Lake Lugano burst its banks in several places and Lake Maggiore threatened to do the same.
Today morning, the main road to Davesco was closed, as were a number of other roads around Lake Lugano, the ATS news agency reported.
Another landslide reportedly forced the evacuation of residents in Chiasso.
The deluge had already forced the closure of a number of roads in recent days, and flooded basements and forced evacuations of medical patients in the area.
Last week, a landslide swept away a house in the Lugano region, killing a young mother and her three-year-old daughter.