Donald Trump once again stirred controversy on Thursday, when he reportedly proposed the creation of a federal database of Muslim residents of the United States.

"I would certainly implement that, absolutely," the real estate tycoon said after a campaign appearance in Iowa on Thursday night, Reuters reported. "There should be a lot of systems, beyond databases."

After he was unable to explain how such a database -- widely considered unconstitutional -- would differ from efforts during the last century to track Jews in Nazi Germany, Trump's comment drew immediate fire from wide circles of American society, including his rivals for the Republican Party's 2016 nomination, MSNBC noted.

Former Florida Gov. Jeb Bush, for instance, said the former "Apprentice" star's comments were "just wrong," according to the news channel.

"You talk about internment, you talk about closing mosques, you talk about registering people. That's just wrong," said the brother of President George W. Bush, who as president frequently insisted that Islam was a "religion of peace" following the Sept. 11, 2001, terrorist attacks on New York and Washington.

"I don't care about campaigns," Jeb Bush added. "It's not a question of toughness. It's to manipulate people's angst and their fears. That's not strength, that's weakness."

However, Trump upped the ante by telling Yahoo News he planned to minutely monitor the followers of the religion.

"We're going to have to look at a lot of things very closely. We're going to have to look at the mosques. We're going to have to look very, very carefully," he suggested.

"There should be a lot of systems, beyond databases," Trump added, calling for "good management procedures."

The Council on American-Islamic Relations on Thursday condemned the remarks. The group also chided Trump's closest GOP challenger, former neurosurgeon Ben Carson, who on Thursday addressed the influx of Syrian refugees in the terms of a "rabid dog running around your neighborhood," according to The Wall Street Journal.

"By mainstreaming Islamophobic and unconstitutional policies, Donald Trump and Ben Carson are contributing to an already toxic environment that may be difficult to correct once their political ambitions have been satisfied," said Robert McCaw, the council's government affairs manager.