The two children died in hospital, where they were rushed to by passersby, while the 49-year-old father died instantly, Italian news agency ANSA reported quoting police in the northern city of Brescia.
The mother of the children was at home when the man carried out the beastly act, the agency said. The man, who was not identified by the police, had an argument with his wife beforehand.
ANSA said the man had lost his job a year ago, but it was not clear if the act was a desperation for economic difficulties.
Italy, which is going through a recession, has witnessed a rash of suicides in recent weeks.
