"Clearly, we have to have a conversation that includes all elements more access to mental health treatment, school safety, and yes, even tighter gun regulations," she wrote. "We all should be willing to talk about any and all solutions that might stop these senseless killings."
Moss subsequently said she's not planning on carrying legislation but didn't rule it out either.
"I'm not going to be quiet about it," she said. "I just haven't made up my mind on what I want to do yet."
Utah law allows concealed weapons permit holders to possess a firearm on any public school campus, including elementary schools, high schools and colleges. In 2011, the Utah Legislature passed a bill that removed the gun-free zone around public schools.
There has, however, been a lack of clarity on whether a permit holder can openly display their weapon on a school campus, according to Utah Attorney General Mark Shurtleff.
"We definitely think the law is vague and we've encouraged the Legislature to clarify it," he said.
Under the law, teachers who are Utah concealed weapons permit holders can be armed and Shurtleff said he supports teachers' rights to protect themselves and students with guns.
Moss, a former school teacher, disagreed.
She said she doesn't believe the answer to tragic school shootings is to bring more guns into schools including calls by some to arm teachers or school administrators. Moss said that is a "recipe for disaster."
"What if you made a mistake? I taught high school and there were some kids who were high on drugs," Moss said. "I remember a kid who looked really angry and he was coming toward me what if I had a weapon? What if I had used it?"
Moss said she was only 5-foot-1 and said it probably wouldn't have taken much for her to be overpowered, either, and a gun would just unnecessarily escalate the issue.
Rep. Jennifer Seelig, D-Salt Lake City, said she thinks the issue will come up when Democratic members meet Jan. 12 to discuss the upcoming legislative session. As the elected minority leader for the 2013 session, Seelig said she would like to push for a more "holistic" approach that included a look at resources for mental health as well as existing gun laws.
She said she hopes to see balance in the debate.
"Whenever we have these discussions on guns, it's always about individual rights," Seelig said. "But there also has be a talk about community responsibility. That part always seems to be cut out."
Clark Aposhian, chairman of the Utah Shooting Sports Council, said he understands the desire to do something, but he said he'd be "100 percent against restricting" gun rights.
"It's like running full steam ahead and exerting a lot of effort on gun control or banning assault rifles and figuring if they [ban proponents] put enough effort into it, that will somehow solve something," Aposhian said "We've got news for them no matter how much effort you put into it [gun control], you won't fix it."
Utah Attorney General-elect John Swallow also said he doesn't want to see tougher gun control laws noting the shooter at Sandy Hook used guns that were his mother's. But he agreed the mass shooting did merit a review of how to make schools safer.
"It's kind of difficult to pinpoint exactly who is going to go crazy. But is there something we can do on the ground that would make things a little safer?" Swallow said. "I think that if we are smart, we will talk to anybody who can have the ability to contribute to the discussion."
Lee Davidson contributed to this report.