US and Iraqi forces are making new efforts to take the remaining part of the city of Falluja which is still in insurgent hands.
The official number of casualties is not known
Late on Wednesday the US-led forces claimed to have possession of three-quarters of the city.
The BBC's Paul Wood says they now have taken more than that, and are preparing to attack insurgents south of the main east-west road that divides the city.
The rebels are said to be disorganised and leaderless, but still dangerous.
Our correspondent says that pockets of resistance remain even in areas the US and Iraqi forces have captured.
He adds that mortar and tank fire was constant through the hours of darkness.
Artillery fire and air strikes resumed on Thursday.
Three relatives of Iraqi Prime Minister Iyad Allawi have been seized and threatened with death if the operation is not halted.
In other developments:
- At least four people are killed in a car bomb in a busy shopping area of central Baghdad on Thursday morning
Several people are wounded in a blast in the northern city of Kirkuk, which was thought to have targeted the convoy of Governor Abdulrahman Mustafa.
There is little information on the number of military or civilian casualties in Falluja.
Reports on Wednesday put the US military's total death toll at 11 Americans and two Iraqi government soldiers.
The number of insurgents captured or killed is considered a military secret until the battle is over.
Hundreds of rebels were said to have been killed on Wednesday alone.
An Iraqi journalist inside Falluja, Fadhil Badrani, told the BBC he had seen the bodies of at least six American soldiers, and many dead insurgents.
"I witnessed with my own eyes two tanks and three personnel carriers having been crippled, and about six American dead lying on the ground...
"There are many, many bodies of combatants strewn around. Some have not been moved since the start of the war. The smell of rotten flesh started to spread - it is very frightening."
As Iraqi forces moved through buildings in areas secured by the coalition, they are reported to have found rooms were hostages had been kept and killed.
Iraqi army general Maj Gen Abdul Qader Jassim told reporters the "slaughterhouses" contained weapons, black hoods and compact discs showing footage of hostages being killed.
FALLUJA ASSAULT FACTS
Up to 15,000 US and Iraqi troops involved
Estimated 3,000 Iraqi insurgent and foreign fighters in city
Estimated 50,000 civilians remain out of usual population of some 300,000
But he refused to say if any remains had been found, or if there was any clue to the fate of the foreign hostages still missing, Reuters news agency reported.
Iraqi Prime Minister Iyad Allawi's 75-year-old cousin, Ghazi Allawi, the cousin's wife and their daughter-in-law were kidnapped from their home in Baghdad on Tuesday.
The previously unknown Ansar al-Jihad group said the hostages would die within 48 hours unless the operation in Falluja ended and prisoners were freed.
Mr Allawi's office said in a statement the government's policy would not change.
In another development, the Arabic television station al-Jazeera has aired a videotape with Falluja militants displaying what they claim are 20 Iraqi soldiers taken captive.
In Washington, President George W Bush praised the US-led forces in Falluja for their "hard work... for a free Iraq".
Aid agencies have highlighted the plight of civilians in Falluja where up to 50,000 people remain out of a pre-war population of 300,000.
The Red Cross has urged all combatants to guarantee passage to the wounded.