An Iraqi journalist told Aljazeera the bombing lasted for up to two hours in the al-Azraqiya neighbourhood, north-east of the city on Monday.
Residents also said the strikes destroyed a house in the al-Askari district. They had no word on casualties.
The journalist said "defenders" of the city were preparing for the expected military onslaught on the city after Iyad Allawi said on Sunday a showdown was imminent.
The interim prime minister said the government was still offering an olive branch, but told a news conference: "Our patience is running thin."
The US-backed government says Saddam Hussein loyalists and fighters loyal to al-Qaida ally Abu Musab al-Zarqawi are operating from Falluja and Ramadi, another city west of Baghdad.
Falluja residents deny the claims that such fighters are hiding in the city.
In Ramadi, three people were killed on Monday in some of the fiercest fighting in weeks between US troops and armed fighters, witnesses and hospital officials said.
The clashes broke out in the east of the city around 7am (0400 GMT). Black smoke could be seen rising from buildings as groups of gunmen fired rocket-propelled grenades and mortar rounds amid heavy US shelling.
Eleven people were wounded in
the clashes in Ramadi
Iraqi families began to flee their homes as fighting intensified throughout the morning and witnesses said they saw a US military vehicle ablaze.
On Saturday and Sunday, seven people, including women and children, were killed and 11 wounded in clashes, said hospital director Abd al-Munaim Uthman.
Residents said US artillery had shelled eastern districts and said there had been air strikes.
The military could not immediately be reached for comment.
The commander of a marine battalion near Falluja told reporters earlier, his men were awaiting orders to attack.
"We will continue to probe the enemy's defence until such time as we decide to enter and clear the city," Lieutenant Colonel Willy Buhl said. "And we'll do that when Prime Minister Allawi and President (George) Bush tell us it's time to go."
The US aim is to crush anti-US forces in Falluja and elsewhere before national elections in January.
Iraqi police attacked
Iraqi National Guards came under two attacks in the Ghazaliya area west of Baghdad while on their way to Falluja city on Monday, Aljazeera has learned.
The convoy, backed by US troops,
was on its way to Falluja
In the first, armed men attacked a two-vehicle Iraqi National Guards patrol, destroying one vehicle.
Two people were transferred to hospital, but it was unclear whether they were killed or injured.
The second incident took place about 500 metres from the first. Armed men attacked a US military convoy protecting a group of Iraqi National Guards heading towards Falluja.
A National Guards vehicle and two US Hummer vehicles were destroyed in the attack.
Baghdad deputy killed
In Baghdad armed assailants killed the deputy governor of Baghdad and wounded four of his bodyguards.
Hatim Kamil was assassinated in a drive-by shooting on Monday morning, said Baghdad Governor Ali al-Haidari.
Interior ministry spokesman Colonel Adnan Abd al-Rahman said Kamil was killed when gunmen opened fire on his car in the southern Dura neighbourhood.
Two of his bodyguards were also wounded in the attack, Abd al-Rahman said.
No other details were immediately available on the killing, the latest in a series of attacks targeting officials linked to Iraq's interim government.