Combatting terrorism is more important than finding labels for the attackers, US presidential candidate Hillary Clinton said Monday, brushing back calls for a deadly attack in Orlando to become an argument for a backlash against Islam.

US authorities are still trying to piece together what led Omar Mateen to attack Pulse, a gay nightclub, early Sunday, killing 49 people before he was shot dead by police. Mateen was a known sympathizer of the terrorist group Islamic State, which has since claimed responsibility for the attack.

Islamist terrorism has prompted fears in the United States for more than a decade, especially since the September 11, 2001, attacks in New York and Washington. Donald Trump, the presumptive Republican nominee for president, has fanned the flames, calling for a blanket ban on Muslim immigrants to the US because of fears they might be radicals.

He took to Twitter in the early hours of the investigation to lambast Clinton, who will almost certainly be his Democratic Party opponent, for refusing to condemn "radical Islam" in her initial statements.

But, in a CNN interview Monday morning, Clinton argued that labeling the problem wasn't the real issue.

"I think Donald Trump's rhetoric is quite dangerous," she said.

"Whether you call it radical jihadism or radical Islamism, it doesn't make a difference," she said. "What I don't do, because I think it's dangerous, is to demonize an entire religion, and that plays into Islamic State's hands.

"It's got to be denounced by everyone regardless of religion."

Trump called Sunday for President Barack Obama to step down for not using the phrase "radical Islam" when discussing the attack.

Clinton called on leaders of all political leanings to come together so the investigation can go forward smoothly, without letting Islamic State off the hook.

"This was a terrorist attack. ISIS is claiming responsibility for it," she said, using a common acronym for Islamic State. "Whether they had anything to do with it, they at least seem to have inspired it."

She also laid out the outlines of another disagreement she has with Trump: on gun control.

Trump has strongly backed the right to gun ownership during his campaign. But Clinton argued that states like Florida do not use enough common sense tools - background checks and permit requirements - that might have kept guns out of the hands of people like Mateen.

"I believe strongly that common sense gun safety reform across this country would make a difference," she said.

Trump was set to make more comments Monday, building upon his statements released Sunday.

"What has happened in Orlando is just the beginning. Our leadership is weak and ineffective. I called it and asked for the ban. Must be tough," he wrote then.

He told supporters on Twitter: "I don't want congrats" for "being right on radical Islamic terrorism."

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