KUWAIT CITY, Kuwait —  Looking forward to a second term as defense secretary, Donald H. Rumsfeld (search) said Monday that he hopes to complete the U.S. military mission in Iraq within the next four years.

"The president asked me if I would be willing to stay on, and I told him I would be delighted to do that," Rumsfeld said.

He spoke to reporters traveling with him to Kuwait and then on to Afghanistan for the Tuesday's inauguration of President Hamid Karzai (search). Rumsfeld said he also planned to visit India on this trip.

He did not say how long he planned to stay as defense secretary in President Bush's second term.

Rumsfeld enumerated reasons he agreed to stay, including good health and a good working relationship with Bush. He said he looks forward to continuing work on many unfinished projects and that high on his list is the conflict in Iraq (search).

Asked whether he believed the United States would be gone from Iraq by the end of his next term, Rumsfeld said, "I would certainly expect that to be the case, hope that to be the case."

President Bush has said he would keep troops there as long as they are needed.