INDIANAPOLIS — Gov. Mike Pence of Indiana suggested in a radio interview on Monday that Donald J. Trump’s proposed ban on Muslims from entering the country could be broadened to include other religions, not just Muslims.

In an interview with Charlie Sykes, a Wisconsin talk radio host, Mr. Sykes specifically pressed Mr. Pence on his running mate’s Muslim ban, asking: “So there’s no longer a proposed temporary ban on Muslims? It would be anyone from those countries, including Christians? Jews?”

Mr. Pence, seeming to go beyond even the policy proposed by Mr. Trump, did not rule out barring immigrants from other religions, if they were coming from nations or territories that support terrorism.

“I think what you heard in the convention speech from Donald Trump, what we’ve talked about out on the stump, is that we would temporarily suspend from countries, or territories if you will — the caliphate of ISIS obviously expands beyond one country,” he said. “But to say that individuals that come from regions or countries that have been compromised by terrorism would, that we would suspend that immigration, I think that’s appropriate until we develop a new vetting system.”