One of the suspect’s daughters is in a critical condition after being shot in the head, but she was able to direct police to him.
After a 20-minute chase, the man’s car was surrounded and he gave himself up following a two-hour stand-off.
Police said the incident appeared to have started over a domestic dispute.
“It appears this stems from a domestic issue with a breakup in the family, from what our witness has told us,” a police press spokesman said.
The gunman and his wife were estranged and she was not in the state of Texas at the time, police said.
Police described the suspect as a man in his 30s with a beard who was “cool as a cucumber”.
When approached by officers he was “just sitting in his car looking out at us,” said Sgt Thomas Gilliland.
There followed “two hours of constant talking with a man armed with a pistol to his head and who had just killed six people”.
Police had been called to a house about 18:00 and found three children and two adults dead, a Harris County Sheriff’s Office statement said.
A fourth child died in hospital. The children ranged in age from 4 to 13. The two adults are also believed to be related to the suspect.
Two of the children who died had been adopted.
The suspect’s 15-year old daughter, who alerted police to the shooting, is currently in critical condition in hospital.
She warned police that her father was heading for her grandparents’ home, allowing them to intercept him on the way.
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