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Police are also investigating the death of a young woman who was believed to have been related to the suspect after her body was discovered at a property in Baerum.

"Our investigation shows that the suspect has extreme right-wing views," Rune Skjold, head of section at the Oslo police, said at a press briefing.

"His aim was to incite fear. That doesn't mean that we can conclude that this was an act of terrorism, but we are investigating it as attempted terrorism."

Police boosted security around the country's mosques on Sunday as the country's Muslims celebrate the Eid al-Adha holiday. Uniformed and non-uniformed officers are involved in the operation, although authorities stressed there had been no specific threats.

"We strongly condemn any attack on any religion, whether in a mosque, synagogue or church," Justice Minister Joran Kallmyr said in a statement.

"I expect that police will take necessary measures to ensure that all Muslims can celebrate Eid peacefully and safely."

According to various media reports, the suspect's online postings had referenced other acts of violence, including the mosque attack in Christchurch and the El Paso attack in Texas.

Police confirmed on Sunday that they were looking into his online activity and receiving assistance from Norway's security service, PST.

Norway has been spared major incidents since right-wing extremist Anders Behring Breivik set off a bomb in Oslo and launched a gun attack on a political youth camp at the island of Utoya in 2011, killing 77 people in all.