He also said he would strengthen background checks on people buying firearms, and remove "gun-free" zones near some US schools.
Mr Trump was hosting a group of gun violence survivors at a "listening session" in the White House, as a student-led movement on gun control gains momentum.
The group also included survivors of other gun violence at US schools.
One student, Sam Zeif, said he was on the second floor at Marjory Stoneman Douglas High School in Parkland during the shooting there a week ago, which left 17 students dead.
"I lost my best friend... I don't understand why I can still go into a store and buy a weapon of war," he said.
Mr Trump told the students he would be "very strong on background checks, very strong emphasis on the mental health of somebody.
"It's not going to be talk like it's been in the past," he added. "It's been going on too long, too many instances, we're going to get it done."
He told the group that armed staff would be a huge deterrent to the "cowards" who attack schools.
"If you had a teacher who was adept at firearms," he said, "they could very well end the attack very quickly."
"It's called concealed carry, where a teacher would have a concealed gun on them. They'd go for special training, and they would be there and you would no longer have a gun-free zone," he said.
He also criticised gun-free zones in schools.
"A gun free zone to a maniac, because they're all cowards, a gun-free zone is 'let's go in there and let's attack, because bullets aren't coming back at us."
Mr Trump listened to emotional pleas for change from about 40 students, teachers and families during the session in the executive mansion's state dining room.
Andrew Pollack, whose daughter, Meadow, was among the 17 killed in the Valentine's Day attack in Parkland - the second-deadliest shooting at a US public school - vented his anger.
"We're here because my daughter has no voice," said Mr Pollack.
"She was murdered last week and she was taken from us - shot nine times on the third floor. We, as a country, failed our children."
"I'm pissed!" he added.
Mr Trump's listening session came a day after he directed his administration to take steps to ban gun "bump stocks".
The accessories - which enable a rifle to shoot hundreds of rounds a minute - were used by a gunman who killed 58 concert-goers in Las Vegas last October.
That was the deadliest attack by a lone gunman in US history.
The NRA opposes a total ban on bump stocks, but has said it is open to restrictions on the devices.