(Reuters) - U.S. Defense Secretary Ash Carter said on Friday that a nuclear agreement with Iran must include inspections of its military sites, a position at odds with recent comments by Iran's Supreme Leader.

In an interview with CNN, Carter said the nuclear deal being negotiated between the United States, other world powers and Iran must include ways to verify Tehran's compliance.

"It can't be based on trust. It has to have adequate provisions for inspections," he said, adding inspections "absolutely" would have to include military sites.

A preliminary agreement was reached last week to restrict Iran's nuclear program to ensure it cannot build a bomb. A final deal faces a June 30 deadline and one of the major stumbling blocks appears to be the issue of inspections.

Iranian Supreme Leader Ayatollah Ali Khamenei, who has the final say for Iran on the deal, on Thursday ruled out any "extraordinary supervision measures" over nuclear activities and said military sites could not be inspected.

A U.S. "fact sheet" issued after last week's agreement was reached in Switzerland said the International Atomic Energy Agency would have regular access to all of Iran's nuclear activities.

Carter, who was interviewed in South Korea, also said the United States possessed a conventional bomb that is designed to destroy deep underground targets. Iran has an underground nuclear facility at Fordow.

But he said employing a military option would only set back Tehran's nuclear program by a year. He noted that is about the same amount of time it would take Tehran to build a bomb if it breaks the deal currently being negotiated.

(Reporting by Eric Beech in Washington; Editing by Sandra Maler)