A fierce battle erupted between US forces and Fallujan resistance fighters near a mosque in Falluja's Jolan district on Friday, a Reuters correspondent said.
The sound of machine-gun fire and grenade explosions echoed across the Jolan district and several fighters were seen on a rooftop beside a mosque.
US soldiers said battles were becoming more intense as fighters were trapped in the city.
"It's extremely dangerous right now because the insurgents have nowhere to go, they are just sitting in houses waiting for us to come in," US marine Corporal Will Porter said.
"I'm supposed to shoot into the houses before our troops go in."
Dire humanitarian situation
Falluja residents reported a dire humanitarian situation.
Rasul Ibrahim, a father of three, fled Falluja on foot on Thursday morning and arrived with his wife and children in Habbaniya, about 20km to the west, at night.
'I'm supposed to shoot into the houses before our troops go in'
US marine Corporal Will Porter
He said families left in the city were in desperate need.
"There's no water. People are drinking dirty water. Children are dying. People are eating flour because there's no proper food," he told aid workers in Habbaniya, which has become a refugee camp, with around 2000 families sheltering there.
Speaking to Aljazeera, a doctor in Falluja gave an emotional plea for an end to the fighting.
"I'm one of the few medical cadres that survived last Monday from the massacre," said Dr. Abbas Ali.
"We are in a very tragic situation. Hundreds of dead bodies are spread in the streets. Even the injured are still there. We can not transfer them. We can not do anything to save them.
Residents say there are hundreds
of dead still lying in the streets
"We call on all organizations and the whole world to help us.
"The US forces have asked us through loudspeakers to get out [of the houses] and raise white flags. But all the city's areas are under fierce bombings.
"We don't know what to do, stay in our place which is under bombardment or get out and get shot," Ali said.
The Iraqi Red Crescent Society urged US forces and the Iraqi government to let it deliver food, medicine and water to Falluja, describing conditions there as a "big disaster".
"We call on the Iraqi government and US forces to allow us to do our humanitarian duty to the innocent people," said Red Crescent spokeswoman Firdus al-Ubadi.
'We don't know what to do, stay in our place which is under bombardment or get out and get shot'
Falluja medic Dr. Abbas Ali
"This is their responsibility," she said, adding that judging by reports received from refugees and pictures broadcast on television, Falluja was a "big disaster".
A US military spokesman said the Red Crescent had permission to help the many civilians who have fled Falluja, but could not say if it had been granted access to the city itself.
Air strikes on Mosul
Elsewhere in Iraq violence flared in the north and in Baghdad.
US forces have launched air strikes on Mosul targeting fighters who have attacked police stations and fought fierce street battles this week, the US military said on Friday.
"We have targeted known concentrations of terrorists in specific areas of the city," said Captain Angela Bowman, a spokeswoman for US forces based in the city.
The strikes come as violence flared in northern Iraq with observers saying fighters had arrived in the area after fleeing Falluja.
US marines said the fighting was
On Friday, armed men assassinated a senior police officer in Mosul, Muaffaq Muhammad Daham, and burnt his house down.
A total of nine police stations had been attacked over the last two days, according to a US military spokeswoman.
Three police checkpoints were attacked on Friday and set ablaze along the road linking Iraq's northern oil city of Kirkuk with Tikrit.
Assailants beat up the police at the checkpoints and took their weapons before fleeing the scene, said police colonel Arkan Hamad from Kirkuk.
Separately, police killed one fighter and captured three others following clashes against the police and national guards Baquba, 60km (36 miles) northeast of the Iraqi capital, police said.
In Baghdad, machinegun fire and grenade blasts echoed across the Iraqi capital on Friday as anti-US fighters clashed with Iraqi national guards, witnesses said.
There was no word on casualties in the fighting in the mainly Sunni Muslim Adhamiya district.
Fighters also clashed with US troops in the Abu Ghraib area on Baghdad's western outskirts, residents said.