Presumptive Republican presidential nominee Donald Trump said on Sunday that the United States should consider more racial profiling in law enforcement, after urging harsher policies in the wake of last week's mass shooting in Orlando.

"I think profiling is something that we're going to have to start thinking about as a country," Trump said when asked on CBS whether he supported more profiling of Muslims in America.

"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 added.

Trump, the presumptive Republican nominee for president, received criticism from many within the GOP for his comments on American Muslims after the attack in Orlando that left 49 people dead and scores more injured.

Trump also reiterated his earlier calls for more scrutiny of mosques, suggesting the country could implement something along the lines of the controversial New York City surveillance program, which was shut down after receiving condemnation from civil rights groups.

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

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 November 13.

The Orlando gunman, Omar Mateen, expressed support for Islamic State, but officials believe he was "self-radicalized."

Trump has drawn criticism from many in his Republican Party for calling for a temporary ban on Muslims entering the United States. He also has called for a suspension of immigration from countries with "a proven history of terrorism".

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

House of Representatives Speaker Paul Ryan endorsed Trump but has said a Muslim ban is not in US interests. In an interview with NBCs, Ryan said Republicans weighing whether to vote for Trump should follow their "conscience."