"We've reached the heart of Jolan," Maj Clark Watson said of an area the Marines view as a bastion for die-hard Saddam Hussein loyalists with military training.

"We have pushed through four square kilometres, but it's too early to say we are controlling it," he said. "That will take time because there will always be pockets of resistance."

Helicopters later fired missiles at targets in Jolan before Marine infantry moved back in. A mortar landed near the railway station and small-arms fire crackled as helicopters circled.

Watson, of the 1st Battalion of Marine infantry, said guerrillas were fighting back, but not as hard as expected. US commanders said many fighters probably fled before the onslaught.

US-led forces spearheaded by Marines launched an assault on Fallujah on Monday night aimed at clearing the city of Baathist rebels and foreign fighters said to be holed up there.

Iraq's interim government has vowed to retake rebel-held cities to enable national elections to go ahead in January.

The US firepower raining down on Fallujah is sure to have caused civilian casualties, but no clear figures have emerged.

The International Committee of the Red Cross said it was "very worried" about the plight of the wounded in Fallujah.

"We urge all combatants to guarantee passage to those who need medical care, regardless of whether they are friends or enemies," said spokesman Ahmad al-Raoui.

He said thousands of women, children and old folk who had fled Fallujah needed water, food, medical care and shelter. "They must be allowed to return home as soon as possible."

Marine tanks that forayed down a main road through central Fallujah last night ran into heavy fire. Gunnery Sgt Ishmail Castillo said insurgents had responded to US mortar fire by firing machineguns and rocket-propelled grenades at the American tanks.

The Pentagon said yesterday evening that at least 10 US and two Iraqi soldiers had died in the offensive unleashed by 10 000 US soldiers and Marines and 2 000 Iraqi troops.

The assault on Fallujah, where residents say wounded children are dying from lack of medical help, food shops are closed and power is cut, angered Sunni clerics who urged Iraqis to boycott the elections seen as vital to peace.

Interim Prime Minister Iyad Allawi and his US backers say disgruntled Baathists and militants led by Jordanian al-Qaeda ally Abu Musab al-Zarqawi have turned Fallujah into the epicentre of Iraq's bloody insurgency.

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