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A boy was critically injured and a girl was in satisfactory condition following the shooting at Berrendo Middle School in Roswell on Tuesday morning (local time).
Governor Susana Martinez said the students were in the gymnasium, where they typically hang out before classes start during cold and inclement weather. The 12-year-old opened fire with the shotgun there about 8am before a teacher talked him into dropping the weapon.
However, he was "quickly stopped by one staff member who walked right up to him and asked him to set down the firearm, which he did", Martinez said.
School superintendent Tom Burris said the faculty had participated in "active shooter" training, and they responded appropriately on Tuesday.
"In the 10 seconds that transpired from the time of this thing starting until the teacher had control of the weapon, there was no cowardice," Burris said. "There was protection for our kids. Everyone acted and did their duties today at Berrendo Middle School."
Officials at University Medical Center in Lubbock, Texas, said an 11-year-old boy was flown there in critical condition and a 13-year-old girl arrived in serious condition. Her condition was upgraded to satisfactory on Tuesday evening.
Information from nurses treating the boy indicates he was the shooter's target, hospital spokesman Eric Finley said. There was some confusion about the boy's age, but Finley said his parents told the hospital he is 11.
The governor said a staff member received very minor injuries, but declined medical care because he wanted to stay and help.
The suspected shooter, whom police have not named, was transferred to an Albuquerque psychiatric hospital following a hearing on Tuesday, according to lawyer Robert Gorence, who is representing his family.
On Tuesday night, hundreds of people poured into the Roswell Civic Center for a prayer vigil, including elected officials and law enforcement officers from various agencies. There were many hugs and tears.
Eighth-grader Odiee Carranza said she was walking to the school gym when the shooter bumped into her as he rushed past. She told him to be careful, and he apologised and continued on. The boy ran to the gym, where he pulled a gun from a band instrument case and fired at the students.
"Then he shot up in the sky, then dropped the gun, and then some teacher grabbed the kid that had the gun," Carranza said.
Carranza described the shooter as a "smart kid and a nice kid".
State Police Chief Pete Kassetas said the investigation was in the early stages, and authorities were still looking into a possible motive. He estimated more than 100 students and faculty members needed to be interviewed.
"I don't have a lot of answers as of yet," Kassetas said, adding police believe they have the only individual responsible for the shooting in custody. The suspect's name was not released.
A statement from the state police said authorities responded at 8.11am. The school was placed on lockdown and children were bussed to a nearby mall, where parents picked them up.
Classes were later cancelled and won't resume until Thursday.
Roswell has a population of about 50,000. It is a centre for ranching and farming. The city is perhaps best-known as the site of an alleged UFO crash in 1947.