Danish police believe a shopping centre shooting that left three people dead and four others seriously wounded was not terror-related.

The gunman acted alone and appears to have selected his victims at random, they said on Monday.

Copenhagen chief police inspector Soren Thomassen said the victims - a 17-year-old boy and 17-year-old girl, both Danes, and 47-year-old Russian man - were killed when the gunman opened fire on Sunday afternoon in the Field's shopping centre, one of Scandinavia's biggest.

Four others - two Danish and two Swedish citizens - were treated for gunshot wounds and are in a critical but stable condition, Mr Thomassen said.

Several other people received minor injuries as they fled, he added.

Mr Thomassen said police had no indication that anyone helped the gunman, identified as a 22-year-old Dane.

He said while the motive is unclear, there is nothing suggesting terrorism, and that the suspect would be charged later on Monday with preliminary charges of murder.

In Denmark, preliminary charges are a step short of formal charges but allow authorities to keep criminal suspects in custody during an investigation.

"There is nothing in our investigation, or the documents we have reviewed, or the things we have found, or the witnesses' statements we have gotten, that can substantiate that this is an act of terrorism," Mr Thomassen said.

Police said they seized a rifle from the suspect who also carried a knife.

"We also know that he has had access to a gun," said Mr Thomassen, adding: "I will not comment further on it now."

He confirmed that the suspect was known to mental health services but provided no further information.

Danish broadcaster TV2 published a grainy photo of the alleged gunman, a man wearing knee-length shorts, a vest or sleeveless shirt, and holding what appeared to be a rifle in his right hand.

"He seemed very violent and angry," eyewitness Mahdi Al-Wazni told TV2.

"He spoke to me and said it (the rifle) isn't real as I was filming him. He seemed very proud of what he was doing."

Images from the scene showed people running out of the shopping centre in panic.

After the shooting, a big contingent of heavily armed police officers patrolled the area, with several fire department vehicles also parked outside the building.

"It is pure terror. This is awful," said Hans Christian Stoltz, a 53-year-old IT consultant, who was bringing his daughters to see Harry Styles perform at concert scheduled for Sunday night near the shopping centre.

"You might wonder how a person can do this to another human being, but it's beyond ... beyond anything that's possible."

The concert was cancelled due to the shooting.

On Snapchat, Styles wrote: "My team and I pray for everyone involved in the Copenhagen shopping mall shooting. I am shocked. Love H."

It was the worst gun attack in Denmark since February 2015, when a 22-year-old man was killed in a shootout with police after going on a shooting spree in the capital that left two people dead and five police officers wounded.

That attack was believed to have been motivated by Islamic extremism.

Danish Prime Minister Mette Frederiksen called Sunday's shooting a "cruel attack".

"It is incomprehensible. Heartbreaking. Pointless," she said. "Our beautiful and usually so safe capital was changed in a split second."

The multi-storey Field's shopping centre is on the outskirts of Copenhagen, just across from a subway station for a line that connects the city centre with the international airport.

A major motorway also runs adjacent to the shopping centre.

The shooting came a week after a mass shooting in neighbouring Norway, where police said a Norwegian man of Iranian origin opened fire during a LGBTQ festival, killing two and wounding more than 20.