Iraqi forces backed by US helicopter gunships have fought insurgents in the Sunni-dominated Haifa Street area of the capital, Baghdad.
The US said it was part of the new plan to restore security to the capital.
The area was cleared after a day-long offensive in which up to 30 militants were killed. One US soldier also died.
The battle came hours after President George W Bush urged the US to give his new strategy a chance to work, warning of "grievous consequences" of failure.
In his annual State of the Union address to Congress, Mr Bush said that if the US stepped back before Baghdad was secure, "the Iraqi government would be overrun by extremists from all sides".
Bush asks for "a chance"
The new US strategy is to take control of insurgent strongholds and hold them, rather than withdrawing and allowing the areas to be re-taken by militias - Haifa Street is the first test.
An advance guard of 3,200 troops arrived in Baghdad on Sunday, part of President Bush's plan to send an extra 21,500 troops to Iraq.
Machine-gun fire
Haifa Street is a major Baghdad thoroughfare lined with high-rise buildings.
The BBC's Mike Wooldridge in Baghdad says Iraqi and US troops moved in before dawn, meeting mortars, grenades and machine-gun fire. Apache attack helicopters provided air support during two prolonged spells of fierce fighting.
The Iraqi government said up to 30 insurgents were killed and another 27 - from several Arab countries - were detained.
A statement from the US military said that one soldier was killed and two others injured in a combined security operation in Baghdad.
Earlier, a resident of Haifa Street, Naseer, told the BBC Arabic Service that Iraqi civilians were trapped in the area.
"I've got wounded all around me - there are 15 wounded and I don't know how many are dead. We can't share information because we can't go out because of the snipers," he said.
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