Speaking on the Fox Business Network, he also told host Maria Bartiromo that American Muslims should be regularly watched.
“These attacks are not done by Swedish people, that I can tell you. We need surveillance. You need to deal with the mosques, whether you like it or not. We have to be smart, we have to be vigilant.”
In contrast, Democratic candidate Hillary Clinton said on NBC’s Today programme that the US must be “absolutely smart and strong and steady” in its response to the attacks, which killed at least 34 people.
“It's unrealistic to say we're going to completely shut down our borders to everyone,” Mrs Clinton added.