REUTERS/Christopher Aluka Berry
The Republican presidential front-runner made the comments during a wide-ranging interview while signing copies of his campaign book, "Crippled America."
His interviewer, radio host Mike Slater, asked Trump what he thought of Democrats calling for gun control after the Wednesday shooting, which left 14 people dead.
"That looks like another Islamic disaster, I mean, frankly," Trump said.
Trump was apparently pointing to various reports indicating that one of the two suspected shooters had been in touch with Islamic extremists, according to anonymous sources. Both suspects were subsequently killed in a firefight with police.
"It turns out to be another terrorist deal. Hard to believe, right?" Trump asked sarcastically. "No matter where you look, it's the same thing. Then when I say we have to practice vigilance and we have to look at people - and whether you're looking at mosques or not - we have to be smart. They want to be so politically correct, but here's another case where it's Islamic terrorism."
Slater asked Trump to elaborate on what he meant by "looking at mosques."
"You have to look at them," Trump responded. "You have to be vigilant. You have to look. I mean, there's something wrong - something going on, all right?"
Trump has stirred a number of campaign-trail controversies related to Muslims, including his apparent openness to a database of American Muslims and his disputed claim that thousands of Muslims in New Jersey cheered as the World Trade Center buildings collapsed in the September 11, 2001, terrorist attacks.
"You look at this horrible terrorism that's going all over the place, and we have to be vigilant and we have to be smart," Trump told Slater. "We can't allow ourselves to be just decimated. And I have friends that are Muslims, that are very nice people, but they understand there's a big problem. We have a big problem."