"From what we see, we believe that it is doing that," May said.
She also said the deal, formally known as the Joint Comprehensive Plan of Action, should stay in place because she believes it will prevent Iran from gaining a nuclear weapon.
The U.K. and other partners continue to support the deal, which opened up economic cooperation with Iran, despite U.S. threats to sanction any country that did business with Iran.
Dickerson's interview with May will air on "CBS This Morning" on Monday.
Iran and other world powers — the U.S., China, Russia, the U.K., France, Germany and the European Union — reached the deal in 2015. It eased sanctions on Iran in exchange for the country curbing its nuclear program.
The International Atomic Energy Agency (IAEA) regularly checks Iranian nuclear facilities to ensure that the country is keeping to its commitments. The IAEA found at the end of August that Iran was complying with the deal's requirements.
Earlier this year, President Trump, who criticized the deal during his campaign and during the first year of his presidency, followed through on his threat to withdraw from agreement. Signing a presidential memorandum, the president reinstated U.S. nuclear sanctions on the Iranian regime, jumpstarting the "highest level of economic sanctions."
"America will not be held hostage to nuclear blackmail," Mr. Trump said at the time.
May said, "We do agree with the United States that there are other aspects of Iran's behavior that we need to be dealing with." She said ballistic missiles and "the way in which Iran is acting in the region to destabilize the region" are issues that need to be looked at.
"But we also want to ensure that we have a nuclear deal in place that prevents them from getting a nuclear weapon," she said.
"We believe that that should stay in place," she said. "And others involved in putting that deal together believe that it should stay in place."