The gun-rights organization issued the call at a press conference Friday, breaking its silence on last week's shooting rampage at a Connecticut elementary school.
PTA executive director Bill Williams says children need to feel safe to do well at school, and having armed guards would probably make them feel less safe.
He says it would also be a prohibitive drain on a school district's or police department's resources, leading to increased class sizes or cuts in other services - and it probably wouldn't work.
Williams noted the slayings of four armed police officers in a Lakewood, Wash., coffee shop in 2009 in pointing out that being armed doesn't prevent violence. He says, "The more people are armed, the more likely there are going to be gun deaths."