Some U.S. troops scheduled to leave Iraq soon might be kept there longer to deal with the surge in violence, Defense Secretary Donald H. Rumsfeld (search) said Wednesday.

Rumsfeld said the violence, which has claimed nearly three dozen American lives since last weekend, is the work of a few "thugs, gangs and terrorists" and is not a popular uprising over the U.S.-led occupation.

"The number of people involved in those battles is relatively small," Rumsfeld said at a Pentagon news conference, accompanied by Joint Chiefs of Staff Chairman Gen. Richard Myers (search). "There's nothing like an army or large elements of people trying to change the situation. You have a small number of terrorists and militias coupled with some protests," Rumsfeld said.

Myers said the fighting came in two broad categories. West of Baghdad in cities such as Ramadi and Fallujah, the main opposition is "former regime loyalists," including supporters of former president Saddam Hussein (search), and anti-American foreign fighters loyal to Abu Musab al-Zarqawi (search).

In Fallujah, U.S. troops are going after those responsible for last week's deaths and mutilations of four American civilian security officers. Nine people have been arrested, including some of those believed responsible, Rumsfeld said.

In the eastern sections of Baghdad and in a half-dozen cities in southern Iraq, the fighting is the doing of radical Shiite cleric Muqtada al-Sadr and those who support him, Myers said.

Rumsfeld and Myers said al-Sadr had between 1,000 and 6,000 fighters in his militia. It's unclear whether al-Sadr's militia is the only group fighting in those areas, Myers said.

American and coalition forces do not control the holy Shiite city of Najaf in southern Iraq, Rumsfeld said. Iraqis asked the coalition to stay out of the city during a pilgrimage, Rumsfeld said.

Al-Sadr's militia has been active in Najaf.

U.S. forces are in the midst of changes in Iraq, as troops who have stayed for a year are replaced by fresh forces. That gives the United States an advantage for now because there are more troops than there otherwise would be, Rumsfeld said.

"Taking advantage of that increase, we are managing the pace of redeployment to allow those seasoned troops ... to see the current situation through," Rumsfeld said.

The defense secretary refused to say how many troops would stay on in Iraq or how long they might stay. After the briefing, a senior defense official said Gen. John Abizaid, the commander of American forces in the region, has not yet asked for troops to stay.

Rumsfeld and Myers repeatedly referred to al-Sadr as a murderer. Al-Sadr has called on his followers to reject the occupation, and his militia forces are believed to be behind some of the violence in Shiite areas.

While those attacking U.S. and coalition forces share al-Sadr's anti-American philosophy, there's no evidence of nationwide coordination of the fighting, Myers said.

"It's not a Shiite uprising. Sadr has a very small following," he said.