"We're investigating this as an attempt at carrying out an act of terrorism," assistant chief of police Rune Skjold told a news conference.

A gunman armed with multiple weapons opened fire in a mosque near the Norwegian capital, Oslo, wounding one person before being overpowered by worshippers on Saturday afternoon.

Skjold said the suspect - a "young white man" had expressed support for Vidkun Quisling - a Norwegian politician who collaborated with occupying German forces during World War II - as well as anti-immigrant stances.

The man appeared to have acted alone, police said, and had been charged with attempted murder and murder for the time being.

The murder charge relates to the death of a young woman related to the suspect whose body was found in a home in the suburb of Baerum, where the shooting took place. 

Prime Minister Erna Solberg expressed her sympathy with those who were present at the mosque or were affected. 

"It should be safe to go to the mosque, church or other worship places," she said in a statement on Saturday, adding that it was too early to speculate over a possible motive.

On Saturday, Norwegian media reported that the suspect was believed to have put up a post to an online forum hours before the attack where he seemingly praised the assailant in the terror attacks on two mosques in Christchurch, New Zealand, in March in which 51 people were killed.

Norway was the scene of one of the worst-ever attacks by supporters of the far-right in July 2011, when 77 people were killed by Anders Behring Breivik.

Breivik said he was motivated by his hatred of multiculturalism, and detonated a massive bomb after which he opened fire on a gathering of the Labour Party's youth wing on the island of Utoya.