Donald Trump says there are thousands of people living in the United States "sick with hate" and capable of carrying out the sort of massacre that killed at least 50 people in a Florida nightclub.
"We can't let people in. ... We have to be very, very strong," the presumptive Republican presidential nominee said.
"The problem is we have thousands of people right now in our country. You have people that were born in this country who are susceptible to becoming "radicalised," the billionaire told Fox News Channel's Fox & Friends.
Read more: Donald Trump criticised for self-congratulatory tweet after mass shooting
He claimed that there are Muslims living here who "know who they are" and said it was time to "turn them in".
Mr Trump, who got embroiled in controversy early in the presidential campaign when he advocated a ban on Muslims being admitted to the United States, said:"There are people out there with worse intentions than the perpetrator of the shootings in Orlando."
Mr Trump planned to further address the deadliest shooting in modern US history in a campaign speech originally intended to attack Hillary Clinton, the presumptive Democratic nominee.
The switch came a day after Mr Trump called for Ms Clinton to drop out of the race for president if she did not use the words "radical Islam" to describe the Florida nightclub massacre.
Mr Trump will use his talk in New Hampshire to "further address this terrorist attack, immigration and national security", his campaign said.
A gunman wielding an assault-style rifle and handgun opened fire inside a crowded gay nightclub in Orlando early on Sunday, killing at least 50 people before dying in a gunfight with police.
Read more: Orlando Pulse Club shooting - Fears death toll will rise after worst US mass shooting
Another 53 people were hospitalized, most in critical condition. Authorities identified the shooter as Omar Mateen, a 29-year-old US citizen from Fort Pierce, Florida.
Mr Trump's hardline approach to fighting Islamic terrorism was a hallmark of his primary campaign.
Besides proposing a temporary prohibition on foreign Muslims from entering the country, he has and advocated using waterboarding and other harsh interrogation methods to try to stave off future attacks.
In the hours after the Orlando shooting, Mr Trump issued a statement calling on President Barack Obama to resign for refusing "to even say the words radical Islam" in his response to the attack.
He said Ms Clinton should exit the presidential race if she does the same.
In an address from the White House, President Obama called the tragedy an act of terror and hate. He did not talk about religious extremists.
He said the FBI would investigate the shootings in the gay nightclub as terrorism, but added the gunman's motivations were unclear.
On Monday, he said: "We're led by a man that either is not tough, not smart, or he's got something else in mind. People cannot believe that President Obama is acting the way he is and cannot even mention radical Islam."
Like President Obama, Ms Clinton called the shootings acts of terror and hate, but did not use the words radical Islam in a statement released by her campaign.
Instead, she said the country must "redouble our efforts" to defend the country, including "defeating international terror groups, working with allies and partners to go after them wherever they are, countering their attempts to recruit people here and everywhere, and hardening our defences at home".
Ms Clinton later said she is not shying away from using the term "radical Islamism" to describe the attack in Orlando and that she has a plan to address the threat.
But she added that singling out a specific religion and trying to demonise its followers will not protect the United States from the next attack.
Ms Clinton, in a phone interview, told NBC Today that she has a plan to defend the nation from "lone wolf" attacks.
"But I'm not going to demonise and demagogue like Trump because it's plain dangerous," she added.
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