Presidential candidate Donald Trump vowed Monday to "suspend immigration from areas of the world where there is a proven history of terrorism" in the wake of a terrorist attack in Orlando, Florida.

The presumptive nominee of the conservative Republican Party renewed his inflammatory call for a ban on Muslims entering the United States and warned that large-scale immigration from Muslim countries could be a "Trojan horse" for terrorists to gain entry.

Authorities are trying to piece together what led Afghan-American Omar Mateen to attack Pulse, an Orlando gay nightclub, killing 49 people early Sunday before he died in a shootout with police. Mateen told police was a supporter of the Islamic State terrorist group, which has since claimed responsibility for the attack.

Trump vowed to implement tougher screening of would-be immigrants and accused President Barack Obama and Democratic candidate Hillary Clinton of lax policies.

"If we want to remain a free and open society - and we do - then we have to control our border, and we have to do it now," Trump said.

He called for "big consequences" for those who know of potential terrorist plots and do not report them to authorities.

The Orlando massacre is the deadliest terrorist attack in the United States since the September 11, 2001, suicide strikes against New York and Washington, in which nearly 3,000 people were killed.

Trump took to Twitter within hours of the shooting in Orlando to lambast Hillary Clinton, who will almost certainly be his Democratic Party opponent, and accused her of refusing to condemn "radical Islam" in her initial statements.

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

In his remarks Monday, Trump said Clinton had begun using the phrase only in response to his criticism.

Clinton argued that labeling the problem was not the real issue.

"I think Donald Trump's rhetoric is quite dangerous," she told broadcaster CNN.

Combatting terrorism is more important than finding labels for the attackers, Clinton said Monday.

"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."

Clinton called on leaders of all political leanings to come together so the investigation can proceed without letting the Islamic State movement off the hook.

"This was a terrorist attack. [The Islamic State group] is claiming responsibility for it," she said. "Whether they had anything to do with it, they at least seem to have inspired it."

She laid out another policy disagreement she has with Trump on gun control.

Trump has strongly backed the right to gun ownership during his campaign. 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 commonsense gun safety reform across this country would make a difference," she said.

Trump accused Clinton of wanting to take away gun ownership rights and called for people to be able to arm themselves for protection.

Trump vowed to be a better friend to the gay community than Clinton, and said he would protect members of the lesbian, gay, bisexual and transgender community.

"Ask yourself: Who is really the friend of women and the LGBT community, Donald Trump with his actions, or Hillary Clinton with her words?" Trump said. "Clinton wants to allow radical Islamic terrorists to pour into our country - they enslave women and murder gays."

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