No images have been released of Khamenei since an Israeli strike at the start of the war that killed much of his family, including his father and wife.
His first comments came in a statement read out by a television presenter on Thursday. In the statement, he vowed to keep the Strait of Hormuz shut and called on neighbouring countries to close US bases on their territory or risk Iran targeting them.
"We know the new so-called not so supreme leader is wounded and likely disfigured. He put out a statement yesterday. A weak one, actually, but there was no voice and there was no video. It was a written statement," Hegseth told a briefing.
"Iran has plenty of cameras and plenty of voice recorders. Why a written statement? I think you know why. His father - dead. He's scared, he's injured, he's on the run and he lacks legitimacy."
An Iranian official told Reuters on Wednesday that the newly appointed supreme leader was lightly injured but was continuing to operate, after state television described him as war-wounded.
Hegseth was joined by General Dan Caine, the chairman of the Joint Chiefs of Staff, at a briefing in which they emphasised US military strikes to knock out Iran's missile and drone capabilities and its navy.
But despite the US attacks on Iran, more Iranian drones were reported flying into Kuwait, Iraq, the UAE, Bahrain and Oman.
Additionally, four US service members were killed on Friday when a US military refueling aircraft crashed in western Iraq, in an incident the US said involved another aircraft but was not the result of hostile or friendly fire.
Since the US and Israel started carrying out strikes against Iran on February 28, 11 US troops have been killed.
