BAGHDAD (AFP) -- A U.S. and Iraqi drive to wrest back control of Baghdad from illegal militias was meeting little resistance on the ground, but the war plan faced a fight in Washington.

On the first weekly day of Muslim prayers since the Baghdad operation began, American and Iraqi police and military units pushed Friday into central districts that have suffered recent sectarian carnage.

The security plan started making headway just as lawmakers in the U.S. House of Representatives were to vote on a motion criticizing President George W. Bush for sending extra U.S. troops to carry it out.

The non-binding resolution cannot prevent Bush from pushing ahead with his "surge" strategy of sending 21,500 more U.S. soldiers to Iraq, but could augur tougher legislation down the line.

Iraq's Prime Minister Nuri al-Maliki, however, talked to Bush by videophone and said the early days of the plan had seen "dazzling successes".

In Iraq, the number of internally displaced Iraqis could top one million by the end of 2007 if the situation deteriorates further, the International Organization for Migration said in Geneva.

In the past three weeks alone, almost 18,000 people have been displaced in the 15 central and southern governorates of Iraq, the IOM said.

In Baghdad, there was no sign of organized resistance to the joint Iraqi-U.S. operation, though a roadside bomb on the Mohammed al-Qasim highway killed an army officer and wounded a soldier, a defense ministry official said.

"We've got no large scale attacks today, there have been some sporadic small arms fire engagements," said U.S. military spokesman Lieutenant Colonel Scott Bleichwehl.

A column of U.S. armored vehicles accompanied by Iraqi police headed into an administrative area of Rusafa near the Shorja market, where last week more than 70 people were killed by a series of car bombs. "We have operations ongoing in the majority of the security districts, with a focus in Adhamiyah and Rusafa," he told AFP. "I don't have the number of individual patrols but it's in the thousands."

International analysts said Shiite militia and Sunni insurgent groups have decided to keep to the shadows and prepare their next move during the sweep, which was announced in detail two months ago.

"I would suggest that both armed groups ... will lie low for as long as the United States carries out this military action in Baghdad," said Joost Hiltermann of the International Crisis Group.

The decision by the militia to abandon checkpoints and armed patrols in areas like Baghdad's Sadr City neighborhood could be a success for the Iraqi government's attempts to draw hardliners into the political process.