Republican Donald Trump said on Sunday the US should consider more racial profiling, in response to a question about whether he supported greater law enforcement scrutiny of Muslim Americans after the Orlando mass shooting.

"I think profiling is something that we're going to have to start thinking about as a country," Trump told CBS' "Face the Nation."

"You look at Israel and you look at others, and they do it and they do it successfully. And you know, I hate the concept of profiling, but we have to start using common sense," he said when asked if he supported increased profiling of Muslims in America.

Trump made similar comments last December about profiling, the targeting of specific demographic groups for extra scrutiny, after a Muslim American and his wife killed 14 people in San Bernardino, California.

Last week, Trump, the presumptive Republican presidential nominee for the Nov. 8 election, sparked criticism from many in his party for his comments on American Muslims after the Orlando attack on Sunday, in which a US-born Muslim man killed 49 people at a gay nightclub.

In a speech on national security on Monday, Trump stood by his call for a temporary ban on Muslims entering the United States and proposed a suspension of immigration from countries with "a proven history of terrorism."

He also said the Muslim community had to "cooperate with law enforcement and turn in the people who they know are bad."

Hillary Clinton, the presumptive Democratic nominee, has said the comments show Trump is unfit to be president.

The Florida gunman, Omar Mateen, was born in the United States to Afghan parents. During a three-hour siege at the club, he expressed support for Islamic State, but officials believe he was "self-radicalized."

In his interview on Sunday, Trump said there were "red flags" around Mateen, who had been investigated twice by the FBI but ultimately cleared.

Trump also reiterated his support for more scrutiny of mosques, saying that could resemble a controversial New York City surveillance program that has been shut down.

"If you go to France right now, they're doing it in France. In fact, in some instances they're closing down mosques," he said.

Police in France closed some mosques shortly after gunmen aligned with Islamic State militants killed 130 people in Paris in a series of attacks on Nov. 13.

House of Representatives Speaker Paul Ryan endorsed Trump but has said a Muslim ban is not in US interests. In excerpts of an NBC interview released on Friday, Ryan, the top elected US Republican, said Republicans weighing whether to vote for Trump should follow their "conscience."

Trump brushed off the criticism on Sunday and said he would put up his own money for his campaign if needed. "It would be nice if the Republicans stuck together," Trump said in an ABC interview. "I can win, one way or another." – Reuters