A 17-year-old who allegedly stabbed his parents and 12-year-old brother to death on Sunday after feeling "extraneous" and wanting to break "free" is in custody in the Italian city of Milan.

The triple killing, which the youth is thought to have carried out after obsessively listening to the melancholic Beatles ballad The Long and Winding Road, has shocked the nation and led to claims that the tragedy is a symptom of the changing role of the family in modern Italy.

Police say the suspect planned the attacks in advance and carried them out after the family had celebrated the father's 51st birthday at their home in Paderno Dugnano, near Milan.

Investigators said the suspect, who they are calling Riccardo, was from an apparently stable family and had not shown signs of distress or mental illness before the incident, prompting massive speculation in Italy about how such a thing could happen.

A school friend told the Italian daily newspaper Corriere della Sera that Riccardo was a kind boy from a "very normal" family.

Police believe he waited until everyone was asleep before starting his assault.

Local media reported that the boy has since confessed to the killings, and said he carried them out because he wanted to be "free".

Reports said the boy told officers: "I thought one stab would be enough to kill, then I realized it wasn't like that."

Luigi Ruzza, a spokesman for the local police department, said Riccardo was waiting for officers outside his home following the incident, after telephoning police to report the crime.

Prime Minister Giorgia Meloni described the killings as "beyond imagination", while Matteo Lancini, a psychologist, was quoted by The Times newspaper as saying: "Italian parents are asking the question: 'What if it happens to us?'"

Meloni offered one theory as to why Riccardo carried out the killings, saying: "I don't think we have understood what is happening to new generations", with issues created by isolation experienced during the novel coronavirus pandemic lockdown combining with "digital dependency".

The Italian news agency ANSA said the boy told police on Tuesday he had planned the attack but never thought he would go through with it.

"I experienced this unease, this existential angst but I never thought I would go as far as killing anyone, I can't explain what happened that night, unfortunately it did," ANSA quoted him as saying.

The youth, who is being detained in Milan's Beccaria juvenile prison, met his lawyer, Amedeo Rizza, on Tuesday, who later described him as deeply affected by what he had done.

"He is becoming aware of what he has done, even if he can't explain it," Rizza told reporters.