Mullen told a U.S. television network Sunday that a nuclear-armed Iran would be in his words, a "very bad outcome" for the world.
In a separate interview Sunday U.S. Defense Secretary Robert Gates said Iran is in his words, "not close a [nuclear] stockpile and not close to a weapon."
The U.N. nuclear agency said in a report last month that Iran had significantly increased its stockpile of low-enriched uranium since November. Some experts say Iran has enough of the material to convert into high-enriched uranium for one nuclear bomb.
Iran says its nuclear work is peaceful and aimed at generating electricity. An Iranian foreign ministry official, Hossein Sheikh al Islam, said Sunday that Iran's first nuclear power plant at Bushehr will be fully operation in September.
Iranian and Russian experts began testing the plant last Wednesday after years of delays.
Iran built the Bushehr plant with Russian help. It is meant to operate on enriched uranium imported from Russia, rather than on fuel produced in Iran. Western nations fear Iran could use the enrichment process to produce nuclear weapons.
Iran has been enriching uranium at another facility in Natanz, in defiance of U.N. Security Council demands that it stop the work.
The Obama administration has said it will seek to end Iran's nuclear ambitions, preferably through diplomacy.
Some information for this report was provided by AFP and Reuters.