National security adviser John Bolton said Sunday that the Trump administration may end up sanctioning European companies that deal with Iran, and said those sanctions could ultimately convince Europe to pull out of the Iran nuclear agreement.

"It's possible," he said on CNN when asked if U.S. sanctions might hit Europe with sanctions. "It depends on the conduct of other governments."

U.S. sanctions against Europe has become the big looming question about how the U.S. and Europe will handle their split over the Iran nuclear agreement. President Trump decided to leave the deal, and said the U.S. would impose sanctions against any foreign company that does business with Iran in certain sectors.

That could lead to sanctions against European companies that are still adhering to the deal, which in turn will lead to tough questions for Europe about whether to allow those sanctions to hit companies that are doing what's legal in Europe.

Bolton indicated that U.S. sanctions could ultimately convince Europe to pull out of the agreement as well.

"I think the issue here is what the Europeans are going to do," he said. "If they're going to see that it's not in their interest to stay in the deal, we're going to have to watch what the Iranians do. They'd love to stay in the deal."

"I think the Europeans will see that it's in their interest ultimately to come along with us," he added.

Bolton agreed that Europe for now seems intent on staying in the deal, but stressed that this could change if the sanctions bite.

"I think that will sink in, and we'll see what happens then," he said.