CONI's executive committee unanimously backed the bid which it described as an "innovative project" that would that give "the greatest chances of success of the candidature for the whole of Italy," CONI said in a statement.
Milan mayor Giuseppe Sala, however, has already said that, while his city is willing to host events, it does not want any governance role in organising the Games.
CONI had first expressed an interest in bidding for the Games in March.
According to the "masterplan" presented by CONI, Milan and Turin would share ice hockey and speed skating while Milan would also host figure skating and curling.
Cortina would stage ski-jumping, alpine skiing and some sliding events. Smaller Alpine venues such as Bormio, Trento and Livigno would also be used.
Italy's last Olympic bid ended in frustration for CONI two years ago when Rome was forced to pull out of the race to host the 2024 Summer Games after the city council voted to oppose the candidacy.
Four other venues -- Calgary in Canada, Sapporo in Japan, Stockholm, and Erzurum, Turkey -- are involved in the so-called dialogue phase of the bidding process.
A bid from Sion, Switzerland, was derailed after a referendum where Swiss voters rejected a proposal to support it with public finances and a bid centred on Graz, Austria, also dropped out over a lack of public support.
The 2022 Winter Games will be held in Beijing after four other cities dropped out of the race, fearing soaring costs and size of the Olympics, leaving the Chinese capital and Kazakhstan’s Almaty as the only candidates.
More cities dropped out of the race for the 2024 Summer Olympics. The IOC opted to award them directly to Paris and in turn give the 2028 Games to Los Angeles, which had also bid for the 2024 event.
(Writing by Brian Homewood; Editing by Toby Davis)
