US Republican presidential candidate Donald Trump has ratcheted up his rhetoric against Muslims in America, saying he will like to monitor their mosques.

"I want surveillance of certain mosques if that's OK," Trump said on Saturday, speaking at a rally in Birmingham, Alabama. "We've had it before."

On Thursday, Trump said he would be open to having a “Muslim database” in America for security reasons, two days after he said that the US would have "absolutely no choice" but to close down some mosques.

Hours later, the Republican frontrunner doubled down on his previous remarks when asked by NBC News if he would create a national database to register all Muslims living in the US to protect the country against terrorism. “I would certainly implement that, absolutely.”

Trump's comments came in the wake of the Paris attacks that left at least 130 people dead and hundreds more injured on November 13.

Speaking in Birmingham on Saturday, the billionaire businessman also linked current terrorist concerns in the US, following the attacks in France, with 9/11.

"I watched the World Trade Center go down," Trump asserted, adding he watched in New Jersey, "as thousands of people were cheering as the building was coming down."

Trump’s comments have drawn strong criticism from his White House rivals.

Democratic presidential candidates Hillary Clinton and Bernie Sanders called Trump’s anti-Muslim rhetoric “shocking” and “outrageous.”

“This is shocking rhetoric. It should be denounced by all seeking to lead this country,” Clinton tweeted on Saturday.

"What an outrageous and bigoted statement. @realDonaldTrump should be ashamed of himself," Sanders tweeted.

Republican presidential candidates have also criticized Trump over his controversial remarks.

Former Florida Governor Jeb Bush called the prospect of a registry for Muslims "abhorrent." Florida Senator Marco Rubio said the idea was "unnecessary" and not something Americans would support.

Texas Senator Ted Cruz, who has largely avoided criticizing Trump throughout the presidential election campaign, said, "I'm not a fan of government registries of American citizens."

New Jersey Governor Chris Christie said creating a national registry based on religion and closing mosques "will do nothing to keep us safer.”

Ohio Governor John Kasich said requiring people to register with the government because of their religion "strikes against all that we have believed in our nation's history."