TOKYO — A man who threw himself out a second-story window as police pursued him is being investigated in the slayings of three people inside the house and three more this week in the neighborhood near Tokyo, police said Thursday.

Television footage showed the man slashing his arm with a kitchen knife several times while looking out the window, crossing his chest and throwing himself out the window. A 41-year-old mother and her two daughters — ages 7 and 10 — were found stabbed to death downstairs, each of them inside a closet, and police said the suspect apparently broke in.

Police saw the suspect, Jonathan Nakada, in the window while investigating another murder nearby. They also say he is being investigated on suspicion of involvement in the murders of a couple in the neighborhood of Saitama prefecture, just north of Tokyo.

Nakada, 30, originally from Peru, is hospitalized and hasn’t been charged. A motive was not immediately known.

Police were criticized for possibly failing to catch an early signal of criminal activity from the suspect. Just one day before the couple was found stabbed to death, police happened to interview the man, who had been brought in by a fire department official for speaking nonsensically. While at a local police station, Nakada requested a cigarette break and went outside, but never returned.

Hours after he left the police station, a caller reported a trespassing, and police obtained an arrest warrant for Nakada on that allegation. Saitama prefectural police defended themselves by saying investigators had no evidence then to make Nakada a murder suspect.