"I want to make it virtually impossible for anyone who has mental issues to use a gun," Scott said Friday during a news conference at the Florida State Capitol. "I want to make it virtually impossible for anyone who is a danger to themselves or others to use a gun."
The sale of bump stocks will be completely banned under the proposal.
Scott on Tuesday met with members of law enforcement, school administrators, teachers, mental health experts and leaders of various state agencies to discuss school safety and possible changes to gun laws.
Scott also met with students this week.
"He was very open to our ideas," Rain Valladares said. "He didn't say, 'I agree; I disagree.' He just wanted to hear our input on everything."
Student Carlos Rodriguez said he and his classmates will continue to fight for change.
"I'm hopeful and I'm confident that things will go well, because we are one voice -- we are one powerful voice," he said. "This is a movement that was begun by students and is run by students, and this is just one step.”