The proposal by the politically powerful NRA is "irresponsible and dangerous," said Randi Weingarten, president of the 1.5 million-member American Federation of Teachers.
"Schools must be safe sanctuaries, not armed fortresses," she said in a statement. "Anyone who would suggest otherwise doesn't understand that our public schools must first and foremost be places where teachers can safely educate and nurture our students."
During a news conference in Washington, D.C., NRA chief Wayne LaPierre blamed video games, movies and music videos for exposing children to a violent culture.
His comments were the first by the nation's largest gun-rights lobby, with 4.3 million members, since the Dec. 14 slayings of 20 first-graders and six adults at Sandy Hook Elementary in Connecticut,
"The only thing that stops a bad guy with a gun is a good guy with a gun," LaPierre said.
Los Angeles Unified Superintendent John Deasy refused to comment today on the NRA proposal.
Earlier in the week, however, Deasy said officials were studying the feasibility and cost of expanding the 300-member police force so an officer could be assigned to every elementary and middle school. Armed LAUSD officers are already stationed at all high schools in the nation's second-largest school district.
In the meantime, Los Angeles Police Department officers will add stops at elementary and middle schools to their daily patrols.