"My point being that if we get out there and we really lead and it appears that we're making progress, that all of the Arab states and even the non-Arab states who are, I think, beginning to recognize that the jihad movement is global" will join, Carson said.
He suggested that he would shoot down a Russian plane if it violated a U.S.-led no-fly zone over Syria, even when told that the decision could prompt Russia to shoot down a U.S. plane in response.
"If they violate it, we will, in fact, enforce it. We'll see what happens. For us to always be backing down because we're afraid of a conflict, that's not how we became a great nation, Chris," he said.
"If we establish a no-fly zone and we make clear the rules, and they violate it — that's why you have a no-fly zone. That's the very definition of a no-fly zone. You can't fly there."
And he continued to argue that China is directly involved in the Syrian conflict, alleging that the Chinese have sent arms to Syria and that these weapons are "very sophisticated and are obviously going to require support in order to operate."
Carson's foreign-policy abilities are under scrutiny after terrorist attacks in Paris on Friday night. The former neurosurgeon and author is popular among Republicans, with more than 7 in 10 expressing a favorable view in a recent Washington Post-ABC News poll. But as the Paris attacks introduce a new dynamic in the 2016 presidential primary, it remains to be seen whether Carson can build credibility on international affairs.
Carson acknowledged his lack of experience when asked how many troops he would commit to fighting terrorism in the Middle East, a scenario he told reporters on Friday he supported.
"I don't want to put a specific number on it or indicate what types of people there are because those are decisions that, I think, are made by people who have a tremendous amount of military experience and capability," he said Sunday. "For me to pretend like I have all that knowledge and the ability to formulate the specific plans is foolish, and I think anybody else who thinks they know it all is foolish also."
"You have to be willing to recognize that you are not the end-all, but that you are the conduit for the conduct of American policies" as president, he said.
At one point, the interview entered odd territory as Carson suddenly brought up neurological principles in response to a question about whether the United States should allow Syrian refugees to enter the country.
"To bring them over here is ... a suspension of intellect," Carson said. "The reason the human brain has these big frontal lobes as opposed to other animals is because we can engage in rational thought-processing ... Animals, on the other hand, have big brain stems and rudimentary thinking because they react. We don't have to just react, we can think."