A photo of the wreckage taken by Italy's fire service showed the crushed remains of the cable auto in a clearing among a thick patch of pine trees near the summit of the Mottarone peak overlooking Lake Maggiore.
The Stresa-Mottarone cable vehicle carries tourists and local people from the town of Stresa on Lake Maggiore, nearly 1,400 metres above sea level, to the top of the Mottarone mountain.
The 20-minute cable auto ride, popular with tourists, links Stresa with the 1 500-metre summit of the Mottarone mountain, which offers spectacular views of the Alps.
"The fall was obviously significant", Walter Milan of the Alpine rescue service told Rai News 24.
"This is the final toll of the accident as the vehicle was carrying 11 passengers when the disaster happened", Simone Bobbio, a spokesman for Italy's alpine rescue service for the Piedmont region, told Reuters.
The two children were in serious condition and were taken to a Turin hospital, Milan said.
No one at the Alpine rescue service was immediately available to give further details.
The Stresa-Mottarone lift had only recently re-opened following the gradual lifting of coronavirus restrictions.
Mottarone reaches a height of 1,491m (4,900ft) and overlooks several picturesque lakes and the surrounding Alps of Italy's Piedmont region. Milan said a total of 15 people were believed to be in the cable vehicle at the time, though the exact number wasn't certain.
In February 1998, a low-flying U.S. military jet severed a cable at Cavalese, a ski resort in Italy's Dolomites, killing 20 people. The mountain has a small amusement park, Alpyland, and a children's roller coaster with 360-degree views.
The cable auto service first opened in August 1970 after nearly three years of works to replace a cog railway and the journey takes 20 minutes, its website said.