Washington (CNN) Ohio Republican Gov. John Kasich, a prominent critic of President Donald Trump, said Monday that Trump deserves credit for his statement calling for a ban on bump fire stocks.

"If he follows through on that, it's fantastic," Kasich said in an interview on CNN's "Anderson Cooper 360."

He added, "In this case he deserves credit for this, and I hope he'll keep it up."

In the wake of the Florida school shooting earlier this month, Kasich had called for Trump to take action on guns.

Trump has called for arming teachers, has backed some strengthening of the background check system and said Monday that his administration would ban bump stocks, which allow people to fire semiautomatic rifles rapidly, mimicking automatic fire.

Kasich said the current political moment meant pressure on government officials to take some kind of action and that the outspoken students from the Florida shooting deserve "a lot of credit" for the urgency in that discussion.

"We're at a different place, and the public has been stronger and stronger and stronger," Kasich said. "So I think it's really hard for somebody in public life to just get out there and say, 'Oh, well, there's not much we have to do.' "

He also nodded in favor of having some teachers armed, as the President has called for repeatedly. Kasich said armed teachers could be welcome alongside a number of measures, like restraining orders to block access to firearms temporarily for mentally unstable people.

"If there's somebody in a school that says, 'Hey, I'd like to do this,' I don't see any reason to not let them do it," Kasich said of armed teachers.

Asked about his own varying record on guns and the recent altering of his campaign website, Kasich defended himself and mentioned he had drawn anger from gun rights advocates when he voted for the assault weapons ban in the 1990s, but he said he has "signed some gun bills because I favor the Second Amendment."

Kasich said he was working with people to develop his own recommendations on guns, and he conceded that change was far from certain.

"I don't, frankly, know how much I'm going to get done now, but I'm going to do my level best," Kasich said.