"We'll be very strong on background checks, very strong emphasis on the mental health of somebody," Mr Trump told the students from Marjory Stoneman Douglas High School during Wednesday's televised event at the White House.
"It's not going to be talk like it's been in the past," he added.
The US president also endorsed a proposal that has long been backed by the National Rifle Association (NRA), a powerful gun lobby group.
He pledged to look "very strongly" at calls for educators to be armed with guns.
"If you had a teacher who was adept at firearms," he said, "they could very well end the attack very quickly."