British forces suffered a number of casualties, Armed Forces Minister Adam Ingram told parliament on Thursday.
"We have suffered a number of casualties including three fatalities. The process of informing their next of kin is under way," he told lawmakers in a brief statement.
The deaths bring the total number of British soldiers killed in Iraq to 73.
Prime Minister Tony Blair's official spokesman said the premier's "thoughts are with the Black Watch and the families of the Black Watch".
Some 850 British soldiers, mostly from the Black Watch regiment, are stationed at Camp Dogwood, 48km south-west of Baghdad.
The infantry unit recently relocated from the British-controlled sector in southern Iraq to relieve US troops expected to take part in a major assault on Falluja.
US soldiers killed
On the American side, two marines were killed and four wounded in action on Thursday in the Iraqi province of al-Anbar, which houses Ramadi and Falluja, the US military said. While on Friday, one US soldier was killed and another wounded in Balad by a roadside bomb explosion.
In other events, US warplanes launched five air strikes against suspected fighter positions in Falluja in the past 24 hours ahead of an anticipated assault on the Iraqi city, the US military said on Friday.
"Iraqi security forces and the 1st Marine Expeditionary Force
continue to degrade and disrupt anti-Iraqi forces in the Falluja-Ramadi area," a military statement said.
Against this backdrop of rising fatalities, Iraqi interim leader Iyad Allawi has warned anti-US fighters holding out in the town of Falluja that time is running out for them to lay down their arms.
"The window really is closing for a peaceful settlement," he said on Friday after meeting European Union leaders in Brussels.
Iraq's interim leader Iyad Allawi
has put anti-US fighters on notice
"The Falluja people, most of them, have left Falluja. The insurgents and terrorists are still operating there," Allawi said.
"We hope they will come to their senses or we will bring them to justice."
Expectations are mounting of a full military onslaught by US forces soon to flush out the town's anti-US fighters if efforts at a negotiated solution fail.
The city west of Baghdad, which has been labelled a headquarters for Iraq's anti-US uprising, has been ringed by more than 1000 US and Iraqi troops since mid-October.