The latest official details from the Texas Department of Public Safety on Tuesday's mass shooting differed sharply from initial police accounts and raised questions about security measures at the school and the response of law enforcement.

The school district in Uvalde, Texas, about 130 kilometres west of San Antonio, has a standing policy of locking all entrances, including classroom doors, as a safety precaution.

But one student told Reuters some doors were left unlocked the day of the shooting to allow visiting parents to come and go for an awards day event.

The newly detailed chronology came hours after videos emerged showing desperate parents outside Robb Elementary School during the attack.

They pleaded with officers to storm the building, and some fathers had to be restrained.

The human toll of the rampage, the deadliest US school shooting in nearly a decade, deepened with news the husband of one of the slain teachers died of a heart attack on Thursday while preparing for his wife's funeral.

At a briefing for reporters, DPS spokesman Victor Escalon said the 18-year-old gunman, Salvador Ramos, made his way unimpeded on to the school grounds after crashing his pickup truck nearby.

Preliminary police reports had said Ramos, who drove to the school after shooting and wounding his grandmother, was confronted by a school-based police officer as he ran towards the school.

Escalon said no armed officer was present when Ramos arrived at the school.

The suspect crashed his pickup truck nearby, opened fire on two people at a funeral home across the street, then scaled a fence onto school property and walked into one of the buildings through an unlocked rear door at 11.40am local time, Escalon said.

Two responding officers entered the school four minutes later but took cover after Ramos fired multiple rounds at them, he said.

The shooter barricaded himself inside the fourth-grade classroom of his victims - mostly children aged nine or 10 - for an hour before a Border Patrol tactical team breached the room and fatally shot him.

The interval appeared to be at odds with an approach adopted by many law enforcement agencies to confront "active shooters" at schools immediately to stop bloodshed.

In one video posted on Facebook by a man named Angel Ledezma, parents can be seen breaking through yellow police tape and yelling at officers to go into the building.

"It's already been an hour, and they still can't get all the kids out," Ledezma said in the video.

Another video posted on YouTube showed officers restraining at least one adult.

A woman can be heard saying, "Why let the children die? There's shooting in there".

Investigators are still seeking a motive, Escalon said. Ramos had no criminal record and no history of mental illness.

Minutes before the attack he had written an online message saying he was about to "shoot up an elementary school", Governor Greg Abbott said.

The gunman's father, also named Salvador Ramos, expressed remorse for his son's actions in an interview published on Thursday by news site The Daily Beast.

"I just want the people to know I'm sorry, man, what my son did," he was quoted as saying.

"He should've just killed me, you know, instead of doing something like that to someone."

In one of the more chilling accounts of the shooting, a fourth-grade boy who was in the classroom told local TV station KENS5 that the gunman announced his presence when he entered by crouching slightly and saying, "It's time to die".

Miguel Cerrillo, 35, and his 8-year-old daughter, Elena, a third-grader at Robb, said the door the shooter used was usually locked.

"But that day they were not locked because it was awards day, and some parents were coming in through those doors," said Elena, who was in the school at the time of the shooting.

At least 17 people, including children, were injured in the massacre.

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