When asked by Barbara Walters on NBC News if he had any regrets about the policy he announced on Monday, the 69-year-old said: "Not at all. We have to do the right thing."
He went on to say he has "tremendous relationships" with many Muslims, who he insisted completely agreed with his plan.
During the interview and in a series of tweets, the Republican presidential candidate attacked those who have come out against his proposal.
"I'm the worst thing that ever happened to Isis," he declared. "The people in my party fully understand that - they're running against me.
"For the most part, they have no poll numbers. I'm leading by a lot. They get it. They're trying to get publicity for themselves."
He said the shutdown would not have to be lengthy and would last until the US was able to monitor Muslims.
"There are people that have tremendously bad intentions," he said.
"We have to be tough, we have to be smart and we have to be vigilant."
It is the third time Mr Trump has defended his call for a "complete shutdown" on Muslim immigration to the US.
Donald Trump's most controversial quotes
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Following criticism of his controversial campaign statement, he told a cheering crowd: "I. Don't. Care."
He later claimed parts of London were "so radicalised" the city's police force are "afraid for their own lives", defending his remarks to MSNBC.
London Mayor Boris Johnson described the comments as "complete and utter nonsense", saying: "The only reason I wouldn't go to some parts of New York is the real risk of meeting Donald Trump."
An online petition calling for Mr Trump to be banned from entering the UK has more than 60,000 signatures. The Government is obliged to respond to any petition with more than 10,000 signatories.
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