The bodies of three people were recovered following a landslide in the Fontana area of the Maggia valley in the Italian-speaking Ticino state on the southern side of the Swiss Alps.
Both southern and western parts of Switzerland have been affected by heavy rain.
Campsites along the River Maggia have been evacuated, while part of the Visletto road bridge collapsed.
One person was missing in the nearby Lavizzara valley.
Further north, the River Rhone burst its banks in several areas of Valais state, flooding a road and railway line.
Valleys south of the Rhone have been drenched with particularly heavy rain, police said.
The body of a man whose partner had reported him missing was found at a hotel in the Alpine resort of Saas-Grund early on Sunday.
It is believed that floodwater caught him by surprise.
Police said another man had been missing since Saturday evening in the Binn area in the upper Rhone valley close to the Italian border.
Floods, thunderstorms and landslides have also hit various regions in northern Italy.
Italian firefighters in the northern Piedmont region said they carried out about 80 rescue operations, evacuating dozens of people.
Two adults and a three-month-old girl were rescued after rising waters left them stuck in their car between Montanaro and San Benigno Canavese, firefighters said.
In the Valle D’Aosta region, several villages were isolated because of overflowing streams.
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In Greece, dozes of firefighters were battling a wildfire south of Athens on Sunday.
Supported by 17 water-carrying aircraft, they tackled the flames in a sparsely-populated area near the town of Keratea, 22 miles south of the Greek capital.
At least one house was in flames, television footage showed.
Amid hot, windy conditions across much of Greece, dozens of wildfires have broken out and people are advised to stay away from forested areas.
In Turkey, meanwhile, holidaymakers have reportedly been warned they may have to move because of a wildfire.
Helicopters are said to be in use in the Selcuk district of Izmir.
