Norwegian police have arrested a man suspected of "Islamist terrorism" after two people were killed and 21 wounded in shootings near a gay bar in Oslo on Saturday, causing the city's Pride march to be cancelled.

But despite the official march being called off, thousands spontaneously gathered throughout the day to march through the Norwegian capital in a display of unity also seen at Pride marches across Europe.

The suspect, who was already known to security services, was arrested quickly after the shooting started around 1:00 am (0700 HKT on Saturday) in central Oslo.

Norway's domestic intelligence service PST, which is responsible for counter-terrorism, said it was treating the attack as "an act of Islamist terrorism".

The suspect "has a long history of violence and threats," PST's chief Roger Berg said.

The suspect had been on the PST's radar "since 2015 in connection with concerns about his radicalisation" and membership "in an Islamist extremist network", Berg told a news conference.

Intelligence services spoke to the suspect last month, but did not consider him to have "violent intentions", Berg said.

He added that the PST was also aware the suspect had "difficulties with his mental health".

The suspect's lawyer, John Christian Elden, told Norwegian news agency NTB he expected his client to be put under "judicial observation" to determine his mental state, as is usually done in such cases.

The suspect has so far refused to be interviewed by investigators.

Police had earlier said the suspect was a 42-year-old Norwegian man of Iranian descent.

Norwegian media named him as Zaniar Matapour, describing him as a father of Iranian Kurdish origin who arrived in Norway as a child.

The two victims were men in their 50s and 60s, the police said, adding that the injuries of the wounded were not life-threatening.

Police said they received the first reports at 1:14 am and the suspect was arrested just five minutes later, adding that he was quickly apprehended thanks to the "heroic contribution" of bystanders.

Organisers of the Pride march due to take place on Saturday afternoon called it off, saying they were following "clear" recommendations from the police.

Oslo Mayor Raymond Johansen later said that the Pride march -- the first for three years because of the pandemic -- was only postponed and would be held at a later date.

Those who did march on Saturday could be heard shouting: "We're here, we're queer, we won't disappear."

"I think it's fantastic that this march is taking place, otherwise he would have won," a visibly upset participant in her 50s told AFP.

Many people, some in tears, laid rainbow flags and flowers near the scene of the attack, which was cordoned off by police.

Norway's Crown Princess Mette-Marit struggled to hold back her tears when she went to the scene, which was also visited by Prime Minister Jonas Gahr Store and other politicians.

"Today is a day that reminds us that Pride is a day we have to fight for -- the goal has not yet been reached," Trond Petter Aunas said near the scene.

The shootings happened near the London Pub gay club, the Herr Nilsen jazz club and a takeaway food outlet in a central area packed with people on a warm summer night. (AFP)