"I really believe I'd run in there even if I didn't have a weapon," Trump told a group of state governors gathered at the White House.
"And I think most of the people in this room would have done that, too," said the US president, while adding: "You never know until you're tested."
Trump has vocally criticized an armed deputy who failed to intervene in the February 14 Parkland mass shooting, suggesting he was a "coward."
He took up that theme again in his comments to the governors, calling the performance of some Broward County sheriff's deputies "frankly disgusting."
"They weren't exactly Medal of Honor winners," he said.
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Trump reiterated his calls for stronger background checks, more effective responses to early warning signs, greater mental health resources and a ban on so-called "bump stocks," devices designed to make semi-automatic weapons fire at even faster rates.
"Bump stocks, we're writing that out," he said. "I don't care if Congress does it or not, I'm writing it out myself," he said.
The US president also said he met with leaders of the National Rifle Association and told them, "fellows, we have to do something. We have to do background checks."
"If we see a sicko, I don't want him having a gun," he said.
The NRA, which has a strong presence among Trump supporters, has been a zealous defender of the constitutional right to bear arms, fighting even modest gun control proposals.
"There is no bigger fan of the Second Amendment than me and no bigger fan of the NRA," Trump said. "These guys are great people. They're going to do something. And they're going to do it, I think, quickly. I think they want to see it. But we don't want to have sick people having the right to have a gun."
Trump has vowed to press ahead with gun law reform in the wake of the Parkland tragedy, but the White House has yet to announce support for specific legislation in Congress, where enacting federal gun restrictions faces major obstacles.
Lawmakers returned to Washington Monday under intensifying pressure to address the nation's gun violence epidemic, with a new CNN poll showing that 70 percent of Americans now support stricter gun laws, up 18 points since October.
