The three children, all under the age of ten, and a woman were unconscious when emergency services pulled them from the sea at Tromsø in northern Norway on Monday.
A seven-year-old girl was subsequently confirmed to have passed away.
The woman, who was in her 20s, died late on Monday night, the University Hospital of North Norway (UNN) confirmed,.
She is being considered a suspect in the investigation of the incident, police confirmed on Tuesday.
An air ambulance carrying the two surviving children, who are aged four and one year, landed at Oslo’s Gardermoen Airport early on Tuesday morning. They are now being treated at Oslo’s Rikshospitalet. The condition of both is described as “life-threatening”.
Norwegian police received an alarm on Monday evening from a passer-by who had observed a stroller and could see footprints down to the water, according to reports.
Several objects, including boots, were found at the water’s edge.
When police arrived at the scene in Tromsø’s Fagereng area, they found four unconscious persons in the sea. Emergency first aid was given before the woman and children were taken to hospital.
Search teams, including divers and a helicopter, searched for additional people in the water after the initial discovery.
At a press briefing on Tuesday, police said the incident was now being investigated as a criminal act, and also confirmed the woman who died was the children’s mother.
“What was yesterday an investigation has now changed in nature to a criminal case. The mother is being investigated for murder and attempted murder,” Tromsø Police station chief Anita Hermandsen said, according to NRK’s report.
All four are originally from Sudan and have temporary residence permits in Norway, the broadcaster reports.
The father of the children came to Norway in 2015, and the mother in 2017 via family reunification. The family was not previously known to police.
“It is important to point out that the police are still at an early stage. We are working on several hypotheses. One of these is that the mother may have inflicted death on one of the children, and caused the other children to be in critical condition,” Hermandsen said.
The children's father voluntarily attended Tromsø police station for questioning on Monday night. Police have not commented on where he was when the incident happened.
“We cannot go into details of the father’s statements, other than that his status is a witness,” said police attorney Gøril Lund said to NRK.
He is currently also under the care of Tromsø Municipality’s psychological and social care team, the broadcaster writes.