WASHINGTON — President Trump asserted Monday that he would have rushed in to save the students and teachers of Marjory Stoneman Douglas High School from a gunman with an assault weapon, even if he was unarmed at the time of the massacre.

Speaking to a meeting of the country’s governors at the White House, Mr. Trump conceded that “you don’t know until you test it.” But he said he believed he would have exhibited bravery “even if I didn’t have a weapon, and I think most of the people in this room would have done that, too.”

The president’s remarks came during an hourlong televised conversation with the governors in the State Dining Room, during which Mr. Trump continued to grapple publicly with how best to respond to the mass shooting in Parkland, Fla., discussing such things as arming teachers and reopening mental institutions.

As Mr. Trump skipped from one possible solution to another, he mused about the “old days,” when potential criminals could be locked in mental hospitals, and he vowed to ban “bump stocks,” an accessory that can make a semiautomatic weapon fire rapidly, more like an automatic rifle. But he dropped any mention of raising the age required to purchase a rifle to 21 from 18, something he said last week he supported, despite opposition from the National Rifle Association.