British Prime Minister David Cameron touted the Iran nuclear deal as a success and "better than the alternative" and said he still holds out hope that the Iranians will change their behavior with respect to their support of terrorism throughout the world.

"I think that if there wasn't a deal we would face Iran with a nuclear weapon and that would have given a terrible choice to the West about enabling that, allowing that to happen or a very diff decision to take military action," he told Chuck Todd, host of NBC's "Meet the Press" in a taped interview that aired Sunday.

He called the deal a "better outcome" and said it "keeps Iran away from a nuclear weapon."

"It's a successful negotiation for the allies, and I think we should be proud of a good deal done," he said.

Still, he said he and other Western allies are not "starry-eyed" about the "regime that we're dealing with."

Cameron said he spoke to Iranian President Hassan Rouhani Saturday and said he wanted to see a change in their support for the Houthis in Yemen, the Assad regime in Syria and "terrorism in the region."

Contrary to critics who argue the deal would allow Iran to obtain a nuclear weapon after the agreement sunsets in 15 years, the British prime minister said the formal deal includes language saying it is "never acceptable for Iran to have a nuclear weapon."

"Obviously, the time frame for which the safeguards are in place, the inspections are in place, are for a particular period in time," he said. "But the deal says it's to acceptable for Iran to have a nuclear weapon."

"The timeline for them getting a nuclear weapon has gotten longer, not shorter," he added.