"Most of these teachers have no interest or no background that would give them any comfort at all being the primary source of defense," he said on Thursday, the same day the Utah Shooting Sports Council provided free concealed-weapons training to more than 150 Utah educators and school employees.
Stewart also expressed his skepticism of the National Rifle Association's push to have an armed guard or police officer in every public school.
"A lot of people are not comfortable having armed guards at grade schools," said Stewart, who thought doing so would also be an expensive undertaking.
The NRA has suggested it would cost $2 billion to place armed guards in schools, although in a CNN interview on Thursday, NRA President David Keene clarified the group's stance, saying each school should decide how to protect its students.
The NRA endorsed Stewart in Utah's 2nd Congressional District which contains all of Salt Lake City and runs south to St. George after giving him a 92 percent rating on its annual scorecard.
Stewart said he would oppose any legislative attempt to restrict ownership of handguns and other common weapons but could bend on banning high-capacity gun magazines for the sake of having a broader discussion on violence.
"I would consider looking at some of the larger magazines and other things if it gave us an opportunity to talk about the other things as well," he said. "Let's talk about the big picture."
To be clear, Stewart doesn't think banning large gun clips would reduce gun violence or stop the mass shootings that have taken place in movie theaters, college campuses and, most recently, Sandy Hook Elementary School in Newtown, Conn.
"I'm not sure I would oppose that, but I don't think it helps and if it helps it is really on the margin," he said. "These shootings would not have been stopped if they [the shooters] had a 30-round clip or a 10-round clip; either way they were going forward."
But Stewart sees such a legislative proposal as a catalyst for a more detailed discussion of other issues, particularly mental health care, where he believes the nation has failed.
"A large percentage of the people sleeping out in the snow tonight have mental-health issues," he said. "We are not taking care of those folks."
Stewart declined to take a position on a proposed assault-weapons ban, supported by President Barack Obama, until he was able to see the details.
Utah's five other members of Congress oppose an assault-weapons ban and have not voiced support for any specific gun-control measure since the Newtown shootings, though Rep. Jason Chaffetz, R-Utah, appeared on ABC's This Week and said the nation should talk about "the intersection of a lethal weapon and how it relates to mental health."
Editor's Note: This story was changed from the original version to reflect that Stewart was endorsed by the NRA.