The two victims have been identified as a Jakob Abdullahi Hassan, a 14-year-old boy who was a ninth grade student at the Fiskå school in Kristiansand, and Tone Illebekk, a 48-year-old woman who worked at a local daycare.
Illebekk leaves behind two children. Police said she was an ethnic Norwegian.
Hassan was born and raised in Norway with Somali heritage.
Police do not believe that the two victims have any relation to each other.
On Tuesday morning, Agder Police said they have committed all available resources to the case but have not identified any suspects.
“We are working hard and broadly on several fronts. But so far we have no one who stands out as a suspect in the case. Several people were brought in for questioning throughout Monday evening and night, but it has so far not led to a breakthrough in the case,” police spokesman Terje Kaddeberg Skaar said.
According to broadcaster NRK, five of the boy's friends are among those who have spoken with police.
Police are still asking for tips from the public.
“We have no exact time for when the stabbing took place, but we are interested in information and witness sightings around Wilds Minne School in the period just before and after 4pm,” Skaar said.
Police were notified of the stabbings at 4.10pm. The first reports were that a woman and a child were stabbed, and that both were taken to the Hospital of Southern Norway with serious injuries.
The woman was declared dead at 5.46pm and the boy died about 15 minutes later, police said.
Wilds Minne School official Anne Marie Mauland Mansoor told Fædrelandsvennen that no students were directly involved in the incident nor witnessed the fatal stabbings.