"We are devastated, in pain", Marcella Severino, mayor of Stresa, told broadcaster RAI.
The cable vehicle was closed between 2014 and 2016 for maintenance work.
The 20-minute cable vehicle ride, popular with tourists, links Stresa with the 1,500-metre (4,900-foot) summit of the Mottarone mountain, and offers spectacular views of the Alps.
The ministry said the accident appeared to have been caused by a ruptured cable near the top of the route.
The cable vehicle crashed to the ground after a cable broke, according to first reports, while one member of the emergency services said the security brake failed to function.
Italian Prime Minister Mario Draghi described the crash as a "tragic accident" and said he was receiving updates from the minister of infrastructure and transport, as well as local officials.
The eldest of the two children taken to hospital, who was believed to be between nine and 10, died after suffering two cardiac arrests, the hospital said.
A spokesman at the Citta della Salute hospital told AFP the child was in stable condition after being intubated and sedated, but his condition still serious. "Our plan was to go up Mount Mottarone because the view is lovely from there", said Luisa Tesserin, a 27-year-old student from Genoa. He was undergoing surgery to stabilise multiple fractures.
Late past year, further inspections were performed on the cables themselves, including magnetic inspections on the primary cables of the lift: the cable that pulls the cabin up the mountain, the support cable that holds the auto and the rescue cables.
Images from the scene show the wreckage lying in a steep wooded area.
According to authorities, the cable line had been renovated in 2016 and had only recently reopened after coronavirus lockdowns forced the closures of ski lifts across Italy.
"It's a awful moment for me and for our community and I think also for the whole of Italy".
Mottarone reaches a height of 4,900 feet and overlooks a picturesque lake.
That meant the cable auto began quickly falling back and picking up speed before it "ended up catapulted out of the support cables", Gasparini said.
The dual cable system is split into two sections, just over two kilometres between Stresa and Alpino and another three kilometres between Alpino and Mottarone. It consist of two cars - in alternate directions - with each one carrying up to 40 passengers, it added.
Severino said that important maintenance works, including changing the cables, had been carried out in recent years.