Republican presidential candidate Donald Trump said on Monday that he would suspend immigration to the United States from countries "where there is a proven history of terrorism" against the United States, his strongest reaction yet to the Orlando nightclub massacre.

Democratic rival Hillary Clinton warned against demonizing Muslim Americans, offering a starkly different approach to national security as the two candidates clashed in speeches reacting to the slayings at a gay nightclub in which 49 people and the gunman were killed and 53 were wounded. It was the deadliest mass shooting in modern U.S. history.

"The Orlando terrorist may be dead, but the virus that poisoned his mind remains very strong, and we must attack it," Clinton, the Democrats' presumptive nominee for the Nov. 8 election, said in a speech in Cleveland.

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In Manchester, New Hampshire, Trump said that, if elected, he would use executive authority to better control immigration, emphasizing one of the main themes of his campaign for the Nov. 8 general election. He noted that Orlando shooter Omar Mateen, 29, had parents born in Afghanistan.

"I would use this power to protect the American people. When I’m elected, I will suspend immigration from areas of the world where there is a proven history of terrorism against the United States, Europe or our allies until we fully understand how to end these threats," the wealthy businessman said.

Trump also challenged Clinton to explain why she is in favor of accepting refugees from the Syrian civil war, and said his policies would better protect American women, gays and lesbians, Jews and Christians. Trump's support among women and gay voters lags far behind that of Clinton.

"Radical Islam is anti-woman, anti-gay and anti-American," said Trump. "I refuse to allow America to become a place where gay people, Christian people, and Jewish people are the targets of persecution and intimidation by radical Islamic preachers of hate and violence."

Trump also lashed out at President Barack Obama by questioning his motives for refusing to use the term "radical Islamic terrorism" in describing such attacks. He argued that both the president and Clinton were unfit to lead the nation.

Mateen was a U.S.-born son of Afghan immigrants. Armed with an assault rifle and pledging loyalty to militant group Islamic State, he opened fire at a gay nightclub in Orlando early on Sunday.

In proposals for dealing with threats of violence at home and abroad, Clinton called for increased efforts to remove Islamic State propaganda from the internet, more air strikes in the areas held by the militant group and better coordination with allies in the region.

She specifically called out three U.S. allies - Saudi Arabia, Qatar and Kuwait - for allowing its citizens to fund mosques and schools that train jihadists.

She also called for stricter gun control laws, reiterating prior calls to prohibit those on terrorism watch lists from buying guns. She pointed out that while the Federal Bureau of Investigation was aware of Mateen as a possible threat, he was still able to legally purchase a gun.

Clinton has called for a complete ban on assault-style guns.

"It’s important that we stop the terrorists from getting the tools they need to carry out the attacks, and that is especially true when it comes to assault weapons like those used in Orlando and San Bernardino," California, Clinton said, drawing a standing ovation from the crowd.

Clinton called on Americans to come together in the way they did after the Sept. 11, 2001 attacks on the World Trade Center and Pentagon. She pointed out that, at the time, she was a Democratic U.S. senator representing New York, while the U.S. president, New York governor and New York City mayor were all Republicans.

"Americans from all walks of life rallied together with a sense of common purpose on Sept 12. ... We had each others' backs. We did not attack each other, we worked with each other to protect our country and rebuild our city," Clinton said. "It is time to get back to the spirit of those days, the spirit of 9/12, let's keep looking for the best within our country, the best within each of us."