The comment during a town hall in New Hampshire was an apparent reference to hijabs, or headscarfs, that some Muslim women wear.
When the woman urged him to replace Muslims with U.S. military veterans at TSA, Trump said, "And we are looking at that," seemingly indicating he was considering a new policy.
He was more pointed in response to a questioner who told Trump he's "opposed to wasting our military in the Middle East on behalf of Zionist Israel."
Trump told the man: "Israel is a very, very important ally of the United States and we are going to protect them 100% -- 100%. It's our true friend over there."
Later, Trump said: "That was a tough question on Israel. That was nasty. Whoa."
Trump's immediate push back on his questioner's comment was a different tactic than he took in September, when a supporter falsely asserted that President Barack Obama is a Muslim
"We have a problem in this country. It's called Muslims," an unidentified man who spoke at a question-and-answer town hall event in Rochester, New Hampshire, asked the mogul back then. "You know our current president is one. You know he's not even an American."
A seemingly bewildered Trump interrupted the man, chuckling, "We need this question. This is the first question."
"Anyway, we have training camps growing where they want to kill us," the man, wearing a "Trump" T-shirt, continued. "That's my question: When can we get rid of them?"
"We're going to be looking at a lot of different things," Trump replied. "You know, a lot of people are saying that and a lot of people are saying that bad things are happening. We're going to be looking at that and many other things."
The man who complained about "Zionist Israel" also talked abortion. "I'm opposed to the murder of unborn babies being legal," he said, to which Trump responded, "We are with you."
Campaign aides didn't immediately respond to a request for more details on whether Trump meant he opposes abortion rights in all circumstances. He made headlines in March when he suggested in an interview that women who undergo abortion should face "some form of punishment"
should the practice be outlawed, a comment that he quickly backed away from.
Thursday's campaign event was colorful even by Trump's standards. Earlier, when a plane flew overhead, Trump said: "That could be a Mexican plane up there
-- they're getting ready to attack."