US troops have been rounding up suspects in Falluja as fighting rages

US and Iraqi forces have been fighting street by street with rebels armed with rifles and mortars. Ten US and two Iraqi soldiers have been killed so far.

A US general said insurgents suffered "significant" casualties, and a man who fled the city told the BBC the streets were littered with bodies.

Relief groups say they are deeply worried about the fate of civilians.

URBAN WARFARE Techniques, tactics and the history of fighting in cities

Earlier, the US-led troops reached a key objective - a mosque in the northern part of Falluja that the US said was being used as an arms depot and a meeting point for the leaders of the insurgency.

The BBC's Paul Wood - who is with US troops outside Falluja and whose reports are subject to military restrictions - said street battles had been going on in eastern and north-western districts.

He says the battle for the complete possession of the city is about to begin.

Click below for a satellite image of Falluja Enlarge Image

Lt Gen Thomas Metz, the multinational ground force commander in Iraq, that troops were achieving their objectives on or ahead of schedule - but he said the fight for the city was far from over.

"I think we're looking at several more days of tough urban fighting," he told reporters at the Pentagon via a videophone.

But he added that he assumed that many of the insurgent leaders, including Abu Musab al-Zarqawi - the Jordanian militant blamed for car bombings, kidnappings and beheadings - had fled before the assault began.

A BBC Arabic Service reporter in Falluja said on Tuesday evening that US forces had withdrawn from his neighbourhood in the centre of the city, leaving behind some snipers.

I can see heavy street-fighting from my house in the centre of the city - US soldiers are here, moving from house to house Fadhil Badrani BBC Arabic service reporter 'Tragedy engulfs my city'

He said the city was in complete darkness, with the rubble still smouldering from the day's artillery bombardment.

Earlier, he witnessed heavy street fighting, with soldiers moving from house to house.

Interim Prime Minister Iyad Allawi, using the emergency powers he activated on Sunday, has imposed an indefinite night-time curfew on Baghdad.

In other developments:

• Rebels take up positions in the heart of nearby Ramadi, after US troops withdraw from the city, a former insurgent stronghold

• Iraq's largest Sunni-led political party, the Iraqi Islamic Party, pulls out of the interim government in protest at the Falluja assault

• The main association of Sunni clerics calls for a boycott of elections due in January

• The United Nations refugee agency and the International Committee of the Red Cross express concern about the civilians in Falluja

• A suspected car bomb hits an Iraqi National Guard base near the northern city of Kirkuk

• Rebels attack police stations in Baquba, north of Baghdad, wounding a number of officers

• Two US soldiers are killed in a mortar attack at their base in the northern city of Mosul, the US military says

Rebel stronghold

Most of Falluja's 250,000 civilians fled the city before the offensive began, but up to 50,000 are estimated to remain there.

FALLUJA ASSAULT FACTS Up to 15,000 US and Iraqi troops involved Estimated 3,000 Iraqi insurgent and foreign fighters in city Estimated 30,000 civilians remain out of usual population of more than 250,000 In pictures: Falluja offensive Q&A: Falluja tactics Arab media anger

Our correspondent says that despite efforts by US forces to select targets carefully, their use of heavy artillery and tanks is bound to lead to civilian casualties.

Residents say water and electricity have been cut off.

The assault on Falluja is aimed at stabilising Iraq ahead of January's poll.

The Sunni Muslim city has been a hotbed of resistance to US-led troops following the toppling of Saddam Hussein last year.