"Don't wait for the next tragedy to happen," said Sami Rahamim, whose father, the company founder, was among those slain.
But gun rights supporters said banning permit holders from bringing their firearms to the Capitol won't make it safer.
"Gun-free zones offer a target-rich and low-risk environment for people who want to inflict mass harm," said Rob Doar, a firearms instructor and activist with the Gun Owners Civil Rights Alliance. "This is a solution in search of a problem."
Members of the alliance, many wearing maroon T-shirts, packed the hearing room. Some wore openly holstered guns on their hips. The group's president, Hamline University law professor Joseph Olson, said the current system works.
"What you should be afraid of are people who don't have a permit, the people who have snuck into the Capitol and have a long history of doing nasty, evil things ... They are the problem — not us," he said.
Afterward, Prettner Solon told reporters there might be a middle ground, even if the advisory committee hasn't found it yet.
"It may take a while for us to be able to talk about it. People tend to dig their heels in and want to protect their rights on either side of this issue," she said. "There's lots of room for movement. We don't have to jump from one extreme to another extreme. There may be measures that we can take to ensure that there is more safety."