Speaking in Washington on Sunday, he insisted that the number of US troops in Iraq would be reduced back to around 138,000 after Iraq's December 15 elections.
After that, he said, they would remain at that level until US commanders have firm evidence that Iraq's own security forces are capable of managing the security situation.
"The president has said, (top US commander George) Casey has said, I have said repeatedly what the arrangements are and the arrangements are that the passover of responsibility to the Iraqis will be condition based," Rumsfeld said.
His comments came as Representative John Murtha, the Democrat congressman whose call for withdrawing US troops from Iraq set off a furore last week, predicted US forces would leave Iraq before next year's congressional elections.
The Pennsylvania lawmaker, a Vietnam veteran and respected authority on the military, said on NBC's Meet the Press that he expected more people to come around and share his views and that US troops should be withdrawn in 2006.
Asked if that meant US troops would be out of Iraq before November congressional elections, Murtha said" "You have hit it on the head."
Congressman Murtha: The public
is thirsting for an answer
Murtha's comments on Iraq have sparked an escalating counter-offensive from the White House against domestic critics of US action in Iraq.
In an unusually raucous session on Friday, the US House of Representatives defeated a nonbinding resolution calling for an immediate troop withdrawal.
Democrats denounced the vote as a political stunt meant to attack and isolate Murtha.
But Murtha predicted that more and more Americans, in government and private life, would come to the same conclusion he had, that US military occupation was making the situation in Iraq worse and that a political solution was needed.
"I have never seen such an outpouring in the 32 years I've been in Congress of support and people with tears in their eyes, people walking along clapping when I'm walking through
the halls of Congress, saying something needed to be said," Murtha said.
"It's not me. It's the public that's thirsting for an answer to this thing," he added."
"The passover of responsibility to the Iraqis will be condition based."
US Defence Secretary
In recent days US President George Bush and top administration officials have gone on the offensive against critics of the Iraq policy.
Speaking in Beijing on Sunday, Bush was more muted than previous administration criticism of his opponents but remained resolutely defensive over his policy in Iraq.
Congressman Murtha, he said, "is a fine man, a good man who served our country with honour and distinction as a marine in Vietnam and as a US congressman."
Meanwhile, Rumsfeld, who appeared on four Sunday talk shows, said debate about war is and should be part of the democratic process.
But the defence secretary said Murtha's call for an immediate withdrawal would strengthen US enemies and embolden terrorists.
"That would be a terrible thing for our country and for the safety of our people," Rumsfeld said on CNN's Late Edition.
Rumsfeld: Withdrawal would
play into the hands of terrorists
He said that any decision on troop levels would "depend on what takes place on the ground".
"We currently have about 159,000 troops in Iraq, we plan to bring that down to 137,000-138,000 after the elections which has been our base line. We're bulked up right now because of the elections coming up December 15," he said.
Speaking on Fox News on Sunday, Rumsfeld depicted progress in Iraq in both the political and military arenas.
"The Iraqi security forces are doing an excellent job. They're well-respected by the Iraqi people. They're engaged in the fight," he said.
While commending Murtha's record as a veteran and lawmaker, Rumsfeld pointed out that neither Republicans nor Murtha's fellow Democrats had rushed to embrace his ideas.