"The question of motive remains," police from Switzerland's eastern Saint Gallen region said in a statement, stressing: "To date there is no indication this was a terrorist or politically motivated act."
Police spokesman Bruno Metzger told AFP "terrorism is not our main theory" for yesterday afternoon's attack and that "other motives" figured far higher on the list, although he would not say what they were.
A 27-year-old Swiss national used flammable liquid to start a fire on a moving train in eastern Switzerland before stabbing passengers, according to police.
Police said the attack had been caught on video, allowing them to determine that the man had acted alone.
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The victims included two men aged 17 and 50, three women aged 17, 34 and 43 and a six-year-old girl. Dozens of people were on the train at the time of the attack, police said.
Regional police in Switzerland's eastern canton of Saint Gallen said a 34-year-old woman who had been in critical condition since the attack had died of her injuries today morning.
A person who had been on the platform at Salez station was also hurt after rushing in to pull out the attacker -- who was on fire -- out of the train, police said.
"His intervention probably prevented worst," police spokesman Hanspeter Kruesi told the Blick daily, suggesting that more passengers might have been injured.
Metzger said police for the time being would not provide more details on the identities or nationalities of the victims.
Late yesterday, police had searched the home of the suspected attacker, who lives in a canton neighbouring Saint Gallen.
Some 90 rescue workers had taken part in yesterday's operation, including police, firefighters, ambulances and three rescue helicopters, police said.
Saint Gallen prosecutors, who have opened a criminal investigation into the attack, have secured the affected carriage, which is being scrutinised by forensics teams.