The gunman is also dead, he said.
[Previous version, published at 4:42 p.m. ET]
Uvalde Memorial Hospital spokesperson Tom Nordwick earlier said that two people died in the school shooting and that 13 children and a man in his 40s were being treated for injuries.
Videos taken by a bystander, Isaias Melendez, show scores of armed officers at the scene while others flee the school.
The school district said it is canceling all school activities following the shooting.
The FBI and the Bureau of Alcohol, Tobacco, Firearms and Explosives (ATF) are assisting local police with the investigation.
This is a developing story and will be updated.
CNN’s Andy Rose contributed to this report.