In his first speech since President George W. Bush abruptly announced the defence secretary's resignation on Wednesday, Rumsfeld told an audience of university students and soldiers in Kansas that a democratic and peaceful Iraq was "the hope and prayer of everyone involved."
"I will say this: It is very clear that the major combat operations were an enormous success. It is clear that in phase two of this, it has not gone well enough or fast enough," he said.
Rumsfeld pointed to Iraq's constitution, its freely elected government, its functioning schools and hospitals, its stock market and the rise of a free press as evidence of progress.
But he said all that had to be weighed against the sectarian violence and the killings of Muslims by other Muslim extremists, which has created "a much more complex situation."
"And quite honestly, our country does not have experience attempting to impose control and our will over vicious, violent extremists that don't have armies, that don't have navies, don't have air forces and operate in the shadows," he said.
"It is a totally different circumstance," he said in a question-and-answer session after a speech at Kansas State University in Manhattan, Kansas.
Rumsfeld said the president and his new defence secretary will continue to make adjustments in Iraq, but he cautioned that dealing with Muslim extremism will take patience and perseverance, just as the Cold War struggle against communism did.
"If we have the perseverance and the resolve, we will end up seeing the Iraqi people ultimately take control of their country, govern their country, provide security for their country. And certainly that's our hope and our prayer," he said.
In the speech, he emphasised the need for all government agencies to pursue joint strategies against extremism, while building the capacity of friendly Muslim countries to confront it within their borders.
Bush picked Robert Gates to succeed Rumsfeld, giving the former CIA chief a mandate to take a fresh look at what is seen by many as a floundering US strategy in Iraq.
Rumsfeld's surprise resignation came the day after a drubbing by Democrats in US mid-term elections that stripped the Republicans of control of Congress, largely because of voter anger over Iraq.
Asked what grade he would give his performance as secretary of defence, Rumsfeld said: "Oh, I'd let history worry about that."
Myers, his onetime partner at Pentagon press conferences, disputed the widely held view that Rumsfeld gave short shrift to the advice of his senior military advisers. He also praised Rumsfeld's loyalty to his commanders.
"He has had many opportunities to deflect the arrows coming his way to the military. Many opportunities. He has never taken one of those opportunities," Myers said.
"To go back and read about Abu Ghraib, and people wanting to place blame, it would have been easy for the secretary of defence to deflect it to the department to individuals. He never did that.
"He sucked up all those arrows, and continued to lead the department in the way that he knew was right," Myers said.
Myers was referring to the scandal over prisoner abuse at Abu Ghraib prison that came to light in 2004 when photographs surfaced showing scenes of sexual humiliation and physical mistreatment of Iraqi inmates by US military guards.

Copyright AFP (Agence France-Presse), 2006