"The problem is real, but it is being dealt with in an orderly and forceful fashion by coalition forces," he said.
In testimony before the Senate Armed Services Committee, Rumsfeld said the U.S. Army's 3rd Infantry Division, which played a central role in capturing Baghdad in April, is beginning to withdraw from Iraq, and the entire unit will be back in the United States by September.
Rumsfeld said there are now 148,000 American troops in Iraq. He did not say whether the 3rd Infantry Division would be replaced by another U.S. unit, although he said he expects thousands of international soldiers to begin operating in Iraq by late summer or early fall.
In other developments:
The (Portland) Oregonian said in Wednesday editions that families of fallen soldiers gave the newspaper a copy of the report, saying they're frustrated that no one likely will be disciplined.
The newspaper said the unit's commander was exhausted and confused and inadvertently led the convoy into an Iraqi stronghold, a mistake compounded by jammed rifles, failed radio communications and a decision not to equip individual soldiers with grenades and anti-tank weapons.
Initial reports incorrectly said Lynch emptied her rifle fighting off Iraqis before being captured, and that she had been shot and stabbed. Instead, she was severely injured in the crash of a U.S. Humvee.
In his Senate testimony, Rumsfeld said the 3rd Infantry Division's 3rd Brigade has already reached Kuwait and will be heading home this month. The 2nd Brigade will be home in August and the 1st Brigade will return in September, he said.
He said each of the final two brigades to leave Iraq will have been in the Gulf region for 10 months by the time they depart.
In the immediate aftermath of the toppling of the Saddam regime in April it was expected that the 3rd Infantry Division would go home by June.
But they were kept longer because of a surge of anti-U.S. violence in Baghdad and elsewhere in central Iraq. That violence has killed at least 29 American troops since President Bush declared major combat operations over on May 1.
In the latest incident, insurgents in Fallujah, a restive town west of Baghdad, fired two rocket-propelled grenades at American troops. The U.S. military and police in Fallujah said there were no injuries and no arrests made.
The Qatar-based Al-Jazeera satellite station reported a second skirmish in Falluja and a gunbattle in the town of Ramadi, but the U.S. military could confirm neither report.
Attacks on U.S. forces in Iraq have been taking place virtually every day — seven soldiers were wounded and three Iraqis killed in violence late Monday and Tuesday that included grenade, mortar and homemade bomb attacks.
U.S. defense officials have revised upward their count of Americans killed by hostile fire in Iraq since the war began in March to 143, a figure that approaches the 147 killed in the 1991 Gulf War. At least 212 Americans have died in Iraq since the conflict began.
L. Paul Bremer, the top U.S. official in Iraq, said Tuesday that the coalition would not rest until Saddam's fate was determined "His days in Iraq are finished," Bremer said.
On Tuesday, U.S. soldiers raided a building in central Baghdad, following up on a claim by residents that say they thought they saw Saddam driving through the area on Monday, and say the ousted leader was met with cheering and gunfire by supporters.
Bremer stood by Washington's assertion that the violence does not amount to a full-fledged guerrilla war.
He blamed the attacks on remnants of Saddam's Baath party, former members of pro-Saddam militias and terrorists. He acknowledged that some of the attacks, like the fatal shooting of a U.S. soldier at Baghdad University on Sunday, showed "professionalism."