"They ought to be able to make the decision," Huntsman told the Salt Lake Tribune editorial board Thursday.
But Huntsman acknowledged that, until the law is changed, the Legislature controls all statutes and regulations governing firearms.
Former Gov. Mike Leavitt battled conservative lawmakers long and hard over the issue of guns in schools and churches, but lost the fight and eventually dropped the issue.
Huntsman said if elected, he would not spend a great deal of political capital early on to press the gun issue with legislators.
"I'll have that conversation at the right time," he said.
Democratic candidate Scott Matheson Jr., dean of the University of Utah law school, agrees guns and classrooms don't mix.
"My view has consistently been that guns do not belong in schools and places of worship," Matheson said in a separate interview. He added he was not prepared to endorse a specific proposal on the subject.
Huntsman said his priorities as governor would be recharging the state's sluggish economic-development programs, cutting through the thicket of unnecessary government regulations and boosting public schools and higher education.
Huntsman also fingered tax reform as a pressing issue for the state.
If outgoing Gov. Olene Walker's tax-reform group develops a plan to overhaul Utah's taxes for the first time in decades, "I'm here to tell you that the next governor is going to have to expend a lot of political capital in the next year to get it done."
But Huntsman said pushing job growth to the point it meets or exceeds population growth tops his agenda.
"Our state is flat on its back economically," he said.
"On our current trajectory, we cannot afford the [education and transportation] projects that we have upcoming," Huntsman said. "We have no choice other than to be competitive because of the bills we have to pay."
The chairman and chief executive officer of Huntsman Family Holdings Co. said Utah has all the right elements to be competitive, including outstanding research universities. But it needs a governor who can promote the state's image.
The trick, he said, is "getting out the message that we are a state on the move; we're a state that is not just known for wearing strange clothes in southern Utah and marrying a lot of women, but, indeed, for higher education, for our technological savvy and for our entrepreneurial insights and ethic."

