ZURICH (Reuters) - One woman died and two girls were in serious condition a day after an attack on a Swiss train by a man armed with a knife and flammable fluid which also claimed the suspect's life, local police said on Sunday.

The 34-year-old woman and the 27-year-old suspect died from their injuries on Sunday, St Gallen cantonal police said.

Five people were stabbed or suffered burns during an attack by a Swiss man on a train nearing Salez station in St Gallen in northeast Switzerland.

A sixth person suffered smoke inhalation as he came to the aid of the others.

Three victims remained in hospital on Sunday morning, including the two girls in serious condition who are aged 6 and 17 years old.

Police searched the home of the suspect, who lived in a neighboring canton. They said they had found no indication of a politically or terrorist motivated act. "The motive remains unclear," they said in a statement. "There is currently none that can be found."

Police have not released the suspect's name.

(Reporting by Brenna Hughes Neghaiwi; editing by Tom Heneghan and Jason Neely)