The Republican presidential hopeful said people had praised his courage in truthfully highlighting a "problem" that others preferred to ignore.
"Now people are getting involved" in the issue, he told CBS News.
Mr Trump's call, after a shooting in the US, has been widely condemned.
Other Republicans, the White House, and the British Prime Minister David Cameron were highly critical of the comments, which followed the San Bernardino massacre, in which 14 people died.
Democratic presidential candidate and former US Secretary of State Hillary Clinton said that Mr Trump's rhetoric was turning him into the "best recruiter" for the Islamic State militant group.
A propaganda video by Al-Shabab, al-Qaeda's Somali affiliate, used a clip of Mr Trump repeating his call at a campaign rally last month.
During an appearance on CBS News' Face the Nation programme, to be shown on Sunday, Mr Trump was questioned over how his comments had been framed by al-Shabab as an incentive for Muslims to join holy war.
"Look, there's a problem," he said. "I bring it up. Other people have called and say you have guts to bring it up because frankly it's true and nobody wants to get involved.
"People that are on different persuasions than me right now are saying, you know, maybe Trump isn't wrong. We want to examine it."
The video, released by al-Shabab's media wing, also urges African-Americans to convert to Islam and take part in holy war. It says racism, police brutality and anti-Muslim sentiment are rife in the US.
In recent years, several Somali-Americans from Minnesota have gone to fight for al-Shabab in Somalia.
Al-Shabab, which seeks to overthrow Somalia's Western-backed government and impose a strict version of Sharia (Islamic law), has carried out attacks in Kenya and Ethiopia.
Last month's campaign statement from Mr Trump called for a "total and complete shutdown of Muslims" entering the US until the authorities could "figure out what is going on".
The call was issued after a deadly gun attack in San Bernardino, California, by a husband and wife who are thought to have been radicalised.
Donald Trump has again defended his call for a ban on Muslims entering the US after it was used in a propaganda video by Somali militant group al-Shabab.