The state police updated the death toll on Tuesday evening, announcing that four more children were among the dead, for a total of 18. The dead also comprised one instructor.

The assailant was identified by state police as Salvador Ramos, 18. The suspect abandoned his vehicle and entered Robb Elementary School with a handgun and possibly a rifle, Mr. Abbott said.

“He shot and killed horrifically, incomprehensibly, 14 students, and killed a teacher,” Mr. Abbott said.

“It is being reported that the subject shot his grandmother right before he went into the school,” the governor said.

At a news conference on Tuesday afternoon, Pete Arredondo, police chief of the Uvalde Consolidated Independent School District, said that several adults and students had been injured. The school has students in the second through the fourth grades, he said.

“At this point, the investigation is leading to telling us that the suspect did act alone during this heinous crime,” Chief Arredondo said.

Uvalde is a city of about 16,000 people about 84 miles west of San Antonio.

In an earlier update, the hospital said several students from the school were being treated in the emergency room.

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