Investigators have named the suspect as Espen Andersen Braathen, a 37-year-old Danish citizen who has lived for most of his life in Kongsberg, where the attacks took place on Wednesday.

He has acknowledged killing the victims, investigators have said.

He was "transferred into the care of health services after an assessment of his health situation," police said. They did not go into further details on his condition.

Later on Friday, a court ruled he could be held for up to four weeks in pre-trial detention.

Braathen is a convert to Islam who had shown signs of radicalisation, police said. He also has a history of being "in and out" of health institutions, the force added, without elaborating.

He will be subjected to a full psychiatric evaluation, his lawyer Fredrik Neumann said on Thursday.

Police said the attacks took place over "a large area" of Kongsberg, a town and municipality about 70km west of the capital, Oslo.

Four women and one man, aged between 50 and 70, were killed in what police have said appeared to be a random "act of terror" Three others, including an off-duty police officer, were wounded.

A student told Reuters how he and his friends shut themselves in his bedroom as the attacker tried to get into his home.

Police have said Braathen is cooperating with the investigation. Any trial will not take place for months.

Prime Minister Jonas Gahr Stoere, who took office on Thursday after winning elections last month, will visit Kongsberg on Friday with Justice Minister Emilie Enger Mehl.

The death toll was the worst of any attack in Norway since 2011, when far-right extremist Anders Behring Breivik killed 77 people, most of them teenagers at a youth camp.

Australian Associated Press