Police also did not confirm reports that the male student was "showing off" the gun when the accidental shots rang out.
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One student has been killed at a high school in a suburb of Birmingham, Alabama, while another is in critical condition.
Wilson declined to identify either student. But Wilson said the circumstances were under investigation and authorities were seeking any witnesses or surveillance video to determine what had happened.
"Let us do our job", Wilson told reporters. "We'll give you the answers as they come".
He added, "We are asking questions from the staff, the students, anyone who was in that area".
Birmingham Mayor Randall Woodfin said the girl who was killed was a graduating senior who had been accepted into college.
"We are not just talking about some person, talking about losing a part of our future".
It is the first school shooting since that incident took place, and the third this year that left students dead. Our hearts are heavy.