U.S. intelligence found that Iran did not move nuclear material from its Fordo facility before American bombers blasted that site, despite a report to the contrary, Sen. Markwayne Mullin said Monday.

"They are claiming that they moved some material," Mullin said, referring to Israel and Iran, respectively. "Our intelligence report says they didn't," the Oklahoma Republican said in an interview on CNBC's "Squawk Box."

"In fact, we actually believe they stored more of it in Fordo because they believe Fordo was impenetrable," said Mullin, a member of the Senate Armed Services Committee. "They thought it was a safe place to be."

But, he added, "We have the ability to destroy things that people think were undestroyable. And so we think we did a really good job."

"However, if we find out that we didn't, we will be working with our allies to finish the job or we will finish the job," Mullin warned.

The Fordo facility, which is located 300 feet below a mountain southwest of Tehran, was hit by American air strikes on Saturday.

President Donald Trump said the strikes targeting Fordo, as well as two other nuclear facilities at Natanz and Isfahan, had "completely obliterated" Iran's major enrichment facilities.

The New York Times, in a report Sunday, cited two unnamed Israeli officials with knowledge of the situation who said Iran appeared to have moved uranium and equipment from Fordo before the U.S. attack.

But Mullin on Monday said the U.S. had "severely damaged, if not completely destroyed, their ability to have a nuclear weapon."

"We have a really good handle on what we've destroyed," he said.

"We have made it very clear, President Trump has made clear for 10 years, that we will not allow Iran, the world's sponsor of terror, to have a nuclear weapon any way whatsoever," he said.

Mullin said that did not mean the U.S. would insert American troops into Iran.

"That means that we can do this through the air, and work with our allies to finish the job," he said.

"And I believe that we may have to work with Israel to continue to maybe get rid of some of their stockpiles as things come up."

Mullin's comments raise the prospect of a more sustained U.S. engagement in the conflict between Israel and Iran than Trump is publicly discussing so far.

The president did not seek authorization from Congress before undertaking the strikes over the weekend.

But pressure on the White House to more fully engage with Congress could grow this week, especially if it appears the United States is preparing for a second major U.S. military action.