The billionaire said banning Muslims is warranted because the US is "at war" with Islamic extremists.
Republican presidential candidate Donald Trump has defended his controversial proposal calling for a "total and complete shutdown of Muslims entering the United States".
The billionaire rejected criticism of the proposal on US television on Tuesday, and said banning Muslims is warranted because the US is "at war" with Islamic extremists.
And he said what he was proposing is "no different" to President Franklin Roosevelt - who he said was "highly respected by all" despite his wartime policies which included putting Japanese-Americans in internment camps in the US.
He told ABC's Good Morning America: "We are now at war. We have a president who doesn't want to say that."
Mr Trump's campaign team has said the proposal was in response to the level of hatred toward Americans among "large segments of the Muslim population".
The statement said that the ban would last "until our county's representatives can figure out what is going on".
Roger Stone, a former advisor to Mr Trump, said the proposal was "common sense".
He said: "We can be nice or we can be safe. The country's under siege.
"This will be a substantial boost to his numbers."
Several of Mr Trump's Republican rivals have piled criticism on the proposal, including Jeb Bush who suggested the tycoon was "unhinged".
He said: "His 'policy' proposals are not serious."
Lindsey Graham, another of the Republican presidential nomination candidates, tweeted that Trump "has gone from making absurd comments to being downright dangerous with his bombastic rhetoric".
Ari Fleischer, who served as White House press secretary for President George W Bush, said: "So far, every boundary he has pushed has worked out for him.
"I hope Republican voters recognise this time he's gone too far."
A spokeswoman for British Prime Minister David Cameron said: "The Prime Minister completely disagrees with the comments made by Donald Trump, which are divisive, unhelpful and quite simply wrong."
Officials with the Council on American-Islamic Relations (CAIR) were also quick to condemn the proposal, saying it entered into the "realm of the fascist now".
Ibrahim Hooper, the group's national communications director, said: "It should be disturbing not only to American Muslims, but it should be disturbing to all Americans that the leading Republican presidential candidate would issue essentially a fascist statement like this."
The proposal comes amid heightened security concerns in the wake of November's deadly terror attacks in Paris and last week's mass shooting in San Bernardino, California.