At a Pentagon news conference, Rumsfeld shied away from a question whether the operation in Fallujah would be a "final showdown" and said that insurgents holed up in the city were determined to resist.
"I think it's a tough business, and it's going to take time," he said.
US marines laid siege to Fallujah in April but later pulled back after a negotiated agreement. But Rumsfeld suggested the current push would be different.
"I could not imagine that it would stop without being completed," he said.
Go-ahead
He made his remarks as US artillery, war planes and tanks pounded the rebel bastion at the start of an operation by some 12 000 US and Iraqi troops to retake the city.
The onslaught was unleashed after Prime Minister Iyad Allawi announced he had given the go-ahead for the military to retake the city, the symbol of the potent insurgency that is bent on undermining his US-backed interim government.
Both Rumsfeld and General Richard Myers, chair of the US joint chiefs of staff, signalled that other operations were likely against the insurgency in Iraq, where elections are scheduled for January.
Use of force
"This will not be the last use of force in Iraq to rid Iraq of the former regime elements and the foreign fighters who do not want Iraq to be successful," Myers said.
"There will be other opportunities, maybe not as dramatic and as big as Fallujah but other opportunities."
Rumsfeld said it was necessary to eliminate "terrorist" havens such as Fallujah in order for the Allawi government to do its work.
"But I think that it wouldn't be for me to suggest when (is) the last step in this process. I think it's something that's been going on for a period now, it's going on for a period ahead.
"Over time, you'll find that the process of tipping will take place, that more and more of the Iraqis will be angry about the fact that innocent people are being killed by the extremists, a number of them from outside the country, and they won't like it."
Rumsfeld brushed off reports that some of the Iraqi army troops did not show up for battle, saying, "I would characterise it as an isolated problem.
"They did well in Najaf, they did well in Samarra. They did well in the peninsula yesterday (on Sunday). And there have been instances where they have not done so well.
"It seems to me that's not surprising."
He said such problems were common with "new units that have a mixture of people who haven't worked together intimately and haven't developed the kind of confidence you develop over time.
"So I think what one ought to expect from time to time, we're going see this type of thing," adding that some Iraqi army and police forces that had performed well.