"We think they do, quite frankly," Mullen said. "And Iran having a nuclear weapon, I've believed for a long time, is a very, very bad outcome for the region and for the world," he said.
Iran officials in the capital, Tehran, denied that they are pursuing a nuclear weapons arsenal and that the uranium buildup is for peaceful purposes only, the New York Times reported.
A report issued on Feb. 19 by U.N. watchdog the International Atomic Energy Agency found that Iran has reached "nuclear weapons breakout capability" and that previous reports of Iran's total uranium stock underestimated the actual amount by about a third.
Defense Secretary Robert Gates said Sunday on NBC's "Meet the Press" that the Iranians are not capable of rapidly constructing a bomb and that the build-up would happen slowly.
"There is some time," Gates said.
Officials are also paying attention to North Korea's nuclear weapons build-up, but Mullen and Gates have yet to issue a recommendation on how to handle that region, Mullen said.
President Barack Obama's administration is currently working on negotiations with Iran and neighboring regions about the country's nuclear weapons program.
The U.S. "will seek to end Iran's ambition to acquire an illicit nuclear capability and its support for terrorism," CNN reported Ambassador Susan Rice told the U.N. Security Council last week.