Speaking outside Scotland Yard headquarters, Metropolitan police assistant commissioner Mark Rowley said there was no evidence that the 19-year-old suspect had been radicalised.
“While the investigation is not yet complete all of the work we have done so far, increasingly points to this tragic incident as having been triggered by mental health issues,” Rowley said.
“Indeed at this time we believe it was a spontaneous attack and the victims were selected at random.”
Rowley said officers had interviewed the suspect and his family, had searched addresses and liaised with security services.
The woman murdered was an American national, Rowley said. Those injured were Australian, American, Israeli and British.
“This morning we’ve searched addresses in north London and we will search another in south London. I emphasise that so far we’ve found no evidence of radicalisation that would suggest the man in our custody is in anyway motivated by terrorism.”
The suspect is a Norwegian national of Somali origin but there is nothing to suggest his background was connected to the attack, Rowley said.
The man was arrested at the scene after police stunned him with a Taser, following the attack, which began at 10.30pm on Wednesday in Russell Square, near the Imperial Hotel and the British Museum.
The suspect was taken to a south London police station after receiving treatment in hospital.
Rowley said terrorism was an initial line of inquiry because in the “current climate of threat” and with recent events across Europe all possibilities should be considered.
The Metropolitan police commissioner, Sir Bernard Hogan-Howe, said: “Mental health remains a substantial focus for our investigation.”
Hotel guests described hearing screaming from the square below, while witnesses to the aftermath saw a body lying on the floor as armed police scrambled to the scene. Other accounts suggested that the attacker had a motorcycle helmet.
Two women and three men suffered “various injuries” in the incident and were receiving treatment in hospital. Three were discharged on Thursday morning.
The incident in the popular tourist area came amid warnings about the near-inevitability of a terrorist attack in the UK, following a series of incidents across Europe and the Middle East.
The investigation into the stabbings, understood to have occurred on the eastern side of the square, was being led by murder detectives on Thursday with the support of counter-terrorism officers.
Hogan-Howe said: “My thoughts are with the family of the woman who was murdered and those who were injured. A normal night out in our busy capital has ended in horrific circumstances.
“Our investigation is moving very quickly and our detectives have been working hard throughout the night. As we have already made clear, mental health remains a substantial focus for our investigation.”
Officers cordoned off the area overnight and were stopping people entering Bedford Place, just off Russell Square, where the suspect is believed to have been arrested. Forensic officers wearing protective suits examined the scene. Most cordons were lifted on Thursday, with one partial road closure still in place.
Witnesses described how armed police flooded the area after the attack and officers established a large cordon to seal off the square, where a forensics tent was later seen.
Additional police were immediately deployed in the area, which is frequented mainly by students and tourists. Along with the British Museum, the University of London and University College London are very close by. There are numerous hotels and restaurants in the area, including Hotel Russell and the Imperial.
Russell Square is a large garden square with a fountain in the middle and a cafe, and is very busy during the day. Russell Square tube station is located just off the square and the area is a main thoroughfare for buses.
The garden area is usually locked at night and would have closed at about 8.30pm. It was not clear whether it was still open when the stabbings took place, or whether they took place within the square itself or just outside.