"This is shocking rhetoric. It should be denounced by all seeking to lead this country," Clinton said in a tweet, a day after Trump in an interview did not rule out a Muslim database, if elected to power.
Former Florida Governor Jeb Bush, a Republican presidential candidate also denounced the idea.
"You talk about internment, you talk about closing mosques, you talk about registering people - that's just wrong," Bush told CNBC in an interview.
Trump, however, insisted on his idea of a database of the Muslims.
"I would certainly implement that, absolutely," he told the NBC news last night.
Trump was asked by NBC News whether he would support creating a database system to track Muslims.
Trump, leading the polls for the Republican nomination, has issued several controversial remarks about Muslims and Syrian refugees in the wake of last week's attacks in Paris claimed by the Islamic State extremist group.
Democratic presidential aspirant Martin O'Malley also lashed out at Trump.
"When you hear people like Donald Trump talking about wanting to do ID cards based on religion. What the hell is that? I mean, how is that at all American?" O'Malley asked.
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