(CNN) -- Facing widespread outrage over the National Rifle Association's response to the Newtown, Connecticut, school massacre, the group's president Thursday tried to clarify, saying that schools should decide for themselves how to protect their children.
"Some will want police officers there. Others of them will want private security guards," David Keene said in an exclusive CNN interview. "There may be some place they want volunteers to do it. We're willing to work with everybody on those questions."
The nation's largest teachers union liked some of Keene's comments, but said the NRA is ignoring crucial points to prevent school shootings.
Keene's interview came nearly a week after NRA Executive Vice President Wayne LaPierre addressed media -- but did not take questions -- and said that all schools in the United States should immediately have armed officers. That is the only way, LaPierre said, to prevent another massacre like that at Sandy Hook Elementary, which left 20 children and six adults dead.
On December 21, LaPierre called for armed officers in "every single school" and said that action should be taken before children return to school at the start of the year.
"I call on Congress today to act immediately to appropriate whatever is necessary to put armed police officers in every single school in this nation and to do it now to make sure that blanket safety is in place when our kids return to school in January," he said.
LaPierre continued, "Before Congress reconvenes, before we engage in any lengthy debate over legislation, regulation or anything else, as soon as our kids return to school after the holiday break, we need to have every single school in America immediately deploy a protection program proven to work, and by that I mean armed security."
On Thursday, Keene took questions about LaPierre's statements, which were heavily criticized, even by some NRA members.
The NRA boasts 4 million members.
"Whether an individual school wants that kind of protection or doesn't want that kind of protection is really up to the individual school," Keene said. "And when we made that statement, when Wayne LaPierre spoke about a week ago, he suggested that what has to happen, and what should happen, is in every school district, administrators, teachers and parents should sit down and ask what's needed to protect the students in that school."
Keene seemed to be broadening the NRA's position by encouraging wider discussion, said Mo Canady, executive director of the National Association of School Resource Officers, a nonprofit nonpolitical group that trains armed officers in schools.
But Canady is alarmed that the NRA thinks "armed guards" in school is a solution.
In his nationally televised address on December 21, LaPierre said armed guards should work in school like they do at "airports, office buildings, power plants, court houses, even sports stadiums."
"We want some clarification on what he means by armed guard," said Canady. "An officer working in a school has to work with students, be engaged in the school day, develop relationships with students. They must be trained to do that, to be involved."
"We feel that could create more problems than it solves," he said.
While talk continued, in Utah teachers were learning how to shoot.
The Utah Shooting Sports Council and the Utah-based website opsgear.com are offering a free shooting class this week to teachers.
The "Safe to learn Safe to teach" class is free and lasts for six hours, just as extensive as a routine conceal-and-carry training course in the state. The course covers how to handle a firearm, how to carry it and maintain it, and provides information about Utah and federal handgun laws.
Council chairman Clark Aposhian explained why be believes teachers should learn to fire weapons.
"When we talk about more guns, are more guns the answer? Who do you think they call and why do they call the police when something like this happens?" he said on CNN Thursday. "Because they know the police will show up with their guns. The only problem is the police show up a little too late. They have lots of guns and equipment and man power, but just a little too late.
"The first responders at Sandy Hook and in Columbine were the teachers themselves, who put their lives in front of these shooters," he said. "Let's not disarm these folks."
Teachers in Utah have had guns in the classroom for years, he said.
"This is not new for Utah. You just haven't heard about it before," Aposhian said. "Teachers have been carrying firearms in locked drawers for 12 years now. And my opponents will say the dire predictions were going to be that every argument between a teacher and student would result in gunfire.
"That hasn't happened. We haven't had accidental shootings. We haven't had guns left behind. And we also haven't had any [school] gun shootings."
But there are some who oppose the idea.
Former special education teacher Cassie Stoneman told CNN affiliate KSL that having a firearm at school makes her nervous.
"I would be terrified that one of my students would find my weapon and bring it out," she said.
Armed guards, too, are not an absolute solution either, said the National Education Association, an influential teachers' union with 3 million members.
To argue otherwise "denies the tragedy at Columbine," NEA President Dennis Van Roekel told CNN, reacting to Keene's interview. "They had armed guards and it didn't stop the tragedy."
An armed guard watching Colorado's Columbine High School in 1999 was unable to prevent the slayings. The county sheriff's office released an account explaining why.
"At Newtown, the doors were locked," Van Roekel added. "They had a buzzer. They did everything right."
Canady said that the push for armed, trained police officers in American schools goes back to the 1950s. But an effort to put guards in schools was federally funded during the Bill Clinton presidency. School-Based Partnership grants in the 1990s paid police agencies to send officers into schools in order to reduce school-related crimes such as drug dealing or alcohol use on campus.
The grant program awarded more than $17 million to 155 agencies in the late 1990s, according to the U.S. Justice Department.
The program has not been funded recently.
While Van Roekel agreed that it might be wise to return to that, guards in school cannot be the only solution.
"Keene's statement includes good things and neglected points," he said. "The part about how everyone needs to sit down is a good point. What's missing is there are other solutions that should be addressed, including metal health and common sense laws that keep guns out of the hands of people that shouldn't have them."
Van Roekel believes there must be a debate over banning large ammunition magazines like the kind Adam Lanza used to mow down his victims at Sandy Hook Elementary.
LaPierre, at least, seems hesitant to consider that.
He appeared on NBC's Meet the Press a few days after he gave his December 21 statement to reporters.
Banning magazines, LaPierre said, is "not going to make any kid safer."