Five other people were hurt in Saturday's assault in eastern Switzerland, including a six-year-old girl who was seriously injured.
"The question of motive remains," police in the Saint Gallen region said in a statement. "To date there is no indication this was a terrorist or politically-motivated act."
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"Terrorism is not our main theory," police spokesman Bruno Metzger told AFP, adding that "other motives" figured far higher, 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 at about 2:20 pm (1220 GMT) before stabbing passengers.
The incident took place on the line between Buchs and Sennwald near Salez station, not far from the eastern border with Liechtenstein and Austria.
Dozens of people were on the train at the time, police said.
Pictures published by Swiss media on Sunday showed burned-out seats by a blackened window, the seats covered with ash and the upholstery burnt to a crisp, while on the platform was a pool of blood.
Police said images of the attack had been caught on surveillance footage, allowing them to determine that the man had acted alone.
The footage, which was not immediately made public, showed the man, who was carrying a knife, pouring out flammable liquid and setting it alight, police said.
A 34-year-old woman and the assailant died in hospital on Sunday, police said.
The injured, who included two men aged 17 and 50, two women aged 17 and 43 and a six-year-old girl, suffered burns and stab wounds. One of the women and the child were in serious condition, police said.
The woman who died had been doused with a large amount of the flammable liquid, leading to speculation she might have been the target.
But Metzger said he could not confirm that, and another police spokesman Hanspeter Kruesi told AFP it did not appear the attack was directed at a single person.
He said it was unclear if the attacker, who did not have a criminal record, knew any of the victims.
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