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Republican presidential hopeful Donald Trump on Monday vowed to "suspend immigration" from countries with links to terror attacks targeting the United States or its allies, one day after the Florida nightclub massacre in which 49 people were killed.

"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," Trump said during a speech in New Hampshire.

"We cannot continue to allow thousands upon thousands of people to pour into our country, many of whom have the same thought process as this savage killer."

Trump rapped his likely opponent in the US presidential race, Democrat Hillary Clinton, by saying she is pushing to expand immigration and the nation's refugee program to allow in more Syrians.

"Clinton wants to allow radical Islamic terrorists to pour into our country," he said.

"Immigration is a privilege, and we should not let anyone in this country who doesn't support our communities."

Speaking of the Orlando shooter, who was born in New York to Afghan parents, Trump said "the only reason the killer was in America in the first place was because we allowed his family to come here."

"We have a dysfunctional immigration system which does not permit us to know who we let into our country," he added.

Trump on Monday also accused American Muslims of protecting their own, including the Orlando shooter, at the expense of national security.

"People in the area, people in the neighbourhood, they know there's something off with him and they don't report them to the police," Trump told CNN.

"The Muslim community does not report people like this," he said.

Trump has previously accused neighbours and relatives of the San Bernardino attackers, who killed 14 people last December, of not alerting authorities despite knowing the couple had been radicalised.

"We have to get the people that surround these maniacs to start talking," Trump added on ABC.

While the White House on Monday urged Congress to introduce "common sense" gun laws to make it harder for people to get their hands on "a weapon of war," Trump argued that if more club-goers had guns, fewer people would have been killed.

Hours after the attack on Sunday, the provocative billionaire drew criticism and accusation of insensitivity for a tweet in which he claimed to be right on "radical Islamic terrorism".

"Appreciate the congrats for being right on radical Islamic terrorism, I don't want congrats, I want toughness & vigilance. We must be smart!," Trump wrote on Twitter.