Norwegian police said on Sunday that a shooting at a mosque near Oslo is being treated as an "attempted act of terror" and that the suspected gunman harbours far-right, anti-immigrant views.

The suspect entered the mosque in the affluent Oslo suburb of Baerum on Saturday armed with multiple weapons and opened fire before being overpowered by a 65-year-old man who suffered minor injuries.

Hours after the attack, the body of a young woman was found in a home in Baerum and police on Sunday confirmed that it was the suspect's 17-year-old stepsister. Investigators launched a murder investigation into the death.

Oslo's acting chief of the police operation Rune Skjold said the investigation into the shooting showed that the suspect, who has not been named, appeared to hold "far-right" and "anti-immigrant" views.

"We are looking at an attempted act of terror," Skjold told a press conference on Sunday.

Only three people were inside the al-Noor Islamic Centre at the time of the attack, and police said they recovered two firearms from the scene but did not specify which type.

Norway's Prime Minister Erna Solberg called the shooting a "direct attack on Norwegian Muslims".

The country was the scene of one of the worst-ever attacks by a right-wing extremist in July 2011, when 77 people were killed by Anders Behring Breivik.

Online posts about 'race war'

Police said they had tried to question the suspect — described as a young man around 20 years old with a "Norwegian background" who was living in the vicinity of the attack — but he did not want to "give an explanation to police".

The man had been known to police before the incident, but according to Skjold, he could not be described as someone with a "criminal background".

Unni Fries, the suspect's lawyer, declined to offer any further information and told AFP that she needed "much more time to get into the case".

There has been a recent spate of white nationalist attacks in the West, including in the United States and in New Zealand where 51 Muslim worshippers were killed in March at two mosques in the city of Christchurch.

Norway's al-Noor Islamic centre shares its name with the worst-affected mosque in the New Zealand attacks.

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 New Zealand assailant.

In the online post, references were made to a "race war" and it ended with the words "Valhalla awaits," a reference to the afterlife for those who have died in battle in Norse mythology.

The authenticity of the post or the exact identity of its author has not yet been established.

The suspect in the Christchurch killings wrote a hate-filled manifesto in which he said he was influenced by far-right ideologues including Breivik.

Breivik detonated a massive bomb in Oslo that killed eight people and then opened fire on a gathering of the Labour Party's youth wing on the island of Utoya, killing another 69 people, most of them teenagers.

'Attack on Norwegian Muslims'

The attack took place on the eve of the Muslim celebration of Eidul Azha, marking the end of the Muslim pilgrimage Haj, stoking fears among Norway's Muslims.

"The terror attack in Baerum is the result of a long-lasting hate of Muslims that has been allowed to spread in Norway, without Norwegian authorities having taken this development seriously," the Muslim organisation Islamic Council Norway said in a statement.

Oslo police increased security around Sunday's celebrations, including ordering their patrols to be armed, which is generally not the case.

"Many did not come to prayer because they are afraid," Basm Guzlan, a 54-year old believer told AFP.

"I will never let myself be frightened, but I must admit that I am worried... that a terrorist could do harm," he added.

On Sunday morning many non-Muslim Norwegians lined up outside an Oslo mosque to show support.

Some carried signs labelled #theyareus, a hashtag started in the wake of the New Zealand attacks, others said #tryggibonn, which translates to "safe in prayer".

"Muslims should be safe in our country and we want to show that they have support from the Norwegian government and, as I see it, the whole Norwegian people," Prime Minister Solberg said after attending an Eidul Azha celebration in the afternoon.

According to official estimates about 200,000 Muslims lived in Norway in 2016, representing nearly four per cent of the total population.