On Tuesday, the 32-year-old man slightly injured the pedestrians, including seven-month-old twins, in what police called a “deliberate” act.
He was arrested a short time later and identified as someone who already had a criminal record, and who some Norwegian media said had links to far-right groups.
But “it looks now like a common criminal case that does not concern us,” said Martin Bernsen, spokesman for the PST interior security service that handles anti-terrorist matters.
“At this point, we are not treating this as a terrorist matter,” Bernsen told AFP, though he noted that the investigation was at an early stage.
On Tuesday, police recovered a hunting rifle and an Uzi automatic pistol along with a large amount of narcotics in the stolen ambulance.
The suspect's lawyer, Øyvind Bergøy Pedersen, told the daily Verdens Gang that the man was just trying to escape from police and had not deliberately tried to injure onlookers.
The lawyer rejected reported links with far-right groups.
A 25-year-old woman who was with the man was arrested as well.
They had been involved in another accident, during which their vehicle overturned, police said
When emergency services arrived at the scene, the man stole the ambulance while the woman fled.
The incident took place in a residential neighbourhood in northern Oslo, and while trying to get away, the man hit a woman with a pram carrying the twins.
They were taken to a hospital but did not suffer any severe injuries.