Names of the four soldiers who died on Monday in the Baghdad attack were not released, but the US military said they were assigned to the Army's Task Force in Baghdad. No further details were released.
Meanwhile, in the town of Husaiba an American marine was killed during the third US offensive in al-Qaim area, code-named Operation Steel Curtain.
Al-Qaida in Iraq has warned US and Iraqi forces to halt the military offensive in al-Qaim within 24-hours.
"Let them know that the price will be very heavy," al-Qaida said in a statement posted on an internet website. Its authenticity could not be verified.
Earlier on Monday, the US military said a soldier died the day before in a roadside bombing near Tikrit.
That brought to at least 2051 the number of US service members who have died since the Iraq war started in 2003, according to an AP count. At least 24 US troops have died so far this month - most of them due to roadside bombings.
Car bombs target US-led forces
almost on a daily basis
In a statement on Monday on the Husaiba offensive, US Marines said American and Iraqi forces were trying to flush out fighters allegedly holed up in mosques, schools and other public buildings but did not say how much of the town had been secured.
US forces were however conducting house-house searches.
The statement also said at least 36 fighters had been killed since the assault began on Saturday in the town, 320km northwest of Baghdad. A Marine commander gave the same figure on Sunday night.
"We are meeting quite a bit of resistance here in Husaiba but the offensive is going well," Captain Conlon Carabine told CNN on Monday. "Our strategy is basically to kill the insurgents when we come across them."
Carabine said US and Iraqi forces plan to establish a long-term presence in the town once the fighters are routed. "Once we clear this town, we're going to stay in this town," he said. "We're not going to leave this population."
In Baghdad a leading Arab politician, Adnan al-Dulaimi, joined other leaders in condemning the offensive and called on US and Iraqi forces to halt military operations.
Al-Dulaimi urged US and Iraqi commanders "to halt their attacks against cities and take into consideration that innocent people should not be punished because of the actions of others".
Adnan al-Dulaimi has condemned
the US offensive in al-Qaim
Two other politicians - Muhsin Abd al-Hamid and Salih al-Mutlaq - both condemned the Husaiba offensive because of the impact on civilians.
But al-Dulaimi also urged Sunnis not to boycott national elections set for 15 December.
"We will participate in the next elections in order to save Iraq and I call upon all political entities not to boycott the elections," al-Dulaimi added. "We will participate even if our houses were brought down upon us."
Elsewhere, five people, including a woman, were killed and four were wounded on Monday in east Baghdad when a mortar shell exploded near a club for members of the Turkomen ethnic minority, police said. It was unclear if the club was the target.
A roadside bomb killed six policemen and three civilians in the capital's southern Dora neighbourhood, said Mohanad Jawad, an official at Yarmouk Hospital.
In Mosul, three armed men burst into an internet cafe and killed a journalist from the Turkomen minority, Ahmad Husain al-Maliki, police said. The motive was unclear but journalists have been targeted in Mosul in the past.
A car bomb exploded near an Iraqi army unit responsible for guarding oil pipelines south of Kirkuk, killing one Iraqi soldier and wounding 12 others, Iraqi police said.
US President George Bush has meanwhile vigorously defended US interrogation practices in what he calls the war on terror and lobbied against a congressional drive to outlaw torture during a visit to Panama.