"I have not personally in 40 years seen a tragedy in one family that is this horrific," Hickman said.
Documents introduced during a preliminary court hearing Thursday show the 15-year-old girl attempted to close the door to the home after telling Haskell her parents weren't home, according to a report by KPRC-TV in Houston. But he kicked in the door.
Haskell was estranged from a woman related to the couple, Hickman said. Authorities said earlier that Haskell's wife lives in another state. Hickman corrected preliminary accounts given by law enforcement personnel Wednesday night that Haskell was the father of the slain children.
The children killed were two boys ages 4 and 14, plus two girls ages 7 and 9. Their parents were Katie and Stephen Stay, according to court documents. The father, a real estate agent, was 39 and the mother was 33, according to Harris County Sheriff's Deputy Thomas Gilliland.
Haskell "gathered up the children that were here and awaited the arrival of the parents," Hickman told reporters outside the home Thursday. "Some time later the victims were shot in the residence."
Hickman said Haskell "came in the guise of a FedEx driver wearing a FedEx shirt."
Federal Express said in a statement that Haskell had "formerly provided service" for the company, but has not done so since January.
Hickman said that after Haskell left the home the injured teenage girl — also a daughter of the murdered couple — contacted authorities telling them the shooter was en route to shoot other family members.
Law enforcement personnel located Haskell's car and a low-speed chase ensued, ending in a cul-de-sac, Hickman said. A standoff then lasted more than three hours before Haskell exited the car, sank to his knees and surrendered.
Online jail records did not list an attorney for Haskell.
At one point during the standoff tactical officers used a large armored vehicle to ram the front of his car, disabling it. Another armored vehicle was used to ram the rear of the car, preventing any chance of escape.
The sheriff's department said precinct deputy constables were called to the house about 6 p.m. Wednesday and found the parents and three children dead. Another child later died at a hospital.
Gilliland said the teenager was in "very critical condition" at Memorial Hermann Hospital in Houston late Wednesday night.
Gilliland described Haskell after the standoff as "cool as a cucumber." He said that when he and other officers first approached, Haskell was "just sitting in his car looking out at us."
Hickman said Haskell surrendered without resistance.
"He was in the car for 3½ hours. He was worn down like the rest of us," he said.