Iraqi forces backed by US helicopter gunships have fought insurgents in the Sunni-dominated Haifa Street area of the capital, Baghdad.
The operation began at dawn and lasted several hours
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".
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.
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.
In other developments:
- Details emerged about Tuesday's downing of a private US security company helicopter, with US and Iraqi sources saying four of five Americans who died were shot execution-style
- Two US Marines died in combat in Anbar province on Tuesday, the US military said in a statement
- Police retrieved the bodies of 33 tortured people that were found in separate locations in Baghdad
- Four policemen were killed when a bomb struck their patrol in western Baghdad, police said
- A well-known professor and economist, Diya al-Meqoter, was shot dead by gunmen