The proposal came amid rising sectarian and insurgent violence that has forced the United States to keep more troops than planned in Iraq to bolster Iraq's troubled security forces.
Rumsfeld would not say how many more Iraqi security forces would be added to a force that now stands at about 310,000 and had been slated to grow to 325,000.
The US television program CBS News reported on Monday that General George Casey, the commander of US forces in Iraq, was expected to recommend an increase in the size of the Iraqi force of up to 100,000 troops.
But Pentagon officials, who spoke on condition of anonymity, tied the increase to a decision to man Iraqi units at 110 percent, which would require at least another 32,500 troops. They said the 100,000 figure was too high.
Rumsfeld said the proposals were made by the Iraqi government and Casey along with Lieutenant General Martin Dempsey, the US general in charge of training the Iraqi security forces.
"I am very comfortable with the increases they have proposed and the acceleration in achieving some of those targets that they have proposed," Rumsfeld told reporters. "And I understand that the Iraqi government is as well."
"Therefore now it is simply a matter of our pressing forward and getting our portion of the budget up to Congress and working to see that it is executed," he said.
US strategy has long relied on standing up Iraqi forces to take over security duties from US and coalition troops, but the levels of violence and US and Iraqi casualties have continued to climb despite rising numbers of Iraqis in uniform.
US troop levels in Iraq this week hit 150,000, the highest it has been since January when the US force was beefed up for the Iraqi elections.
Iraqi Prime Minister Nuri Al-Maliki has complained bitterly that Iraqi security forces are not well enough equipped and has pressed for direct control over Iraqi forces.
Asserting his authority as commander-in-chief, Maliki on Monday ordered the military to pull down a cordon around Sadr City, a stronghold of a militia loyal to radical Shia cleric Moqtada al-Sadr.
US and Iraqi troops had sealed off the area during a search for a missing Iraqi-American servicemember who was reported to have been kidnapped by the militia.
Rumsfeld said he had seen the reports but would not comment on the situation except to say the Iraqi government had a difficult job.
Details of the new proposals to increase the size of the Iraqi force were sketchy, with Rumsfeld refusing to talk about the numbers, costs or how long commanders believed it would take to achieve.
He said he doubted it would require more US trainers. About 5,000 US troops are current assigned to training missions, many of them embedded with Iraqi units.
Casey said on October 24 that it will take 12 to 18 months for the Iraqi security forces to assume responsibility for security throughout the country. Maliki has been quoted as saying it would take six months if he had more control.
Pentagon officials, speaking on condition of anonymity, said the increase in the Iraqi security forces would be used to make up deficits in chronically undermanned units.
Casey said Iraqi units, which are undermanned to begin with, are another 25 percent below strength at any given moment because of a leave policy that allows soldiers to return home for a week each month after being paid.
The Iraqi defence ministry has put in place a policy that will require commanders to increase unit manning to 110 percent "so when they take the people off for leave, there's still a credible enough force to put in the field," he said.

Copyright AFP (Agence France-Presse), 2006