The Golan district, the scene of heavy fighting over the past few days, was one of the three areas hit on Thursday, according to witnesses.
The warplanes roared low over the city after pounding Golan and the al-Nawwab al-Dhubbat and Nazzal districts in Falluja, some 50km west of Baghdad.
The strikes occurred just hours after US officials and local leaders said a deal had been struck to begin pulling US marines back from parts of the city they now control.
US commanders have been reported as saying a former general with Saddam Hussein's army would supervise a 1100-strong force of Iraqi soldiers.
But Pentagon officials in Washington have been denying knowledge of any such deal.
It was not immediately clear whether the air strikes would have any impact on a possible agreement.
Marines agreed earlier in the day to ease their grip over the besieged city where a month-long siege has cost hundreds of Iraqi lives.
But the latest attacks appear to give credence to suggestions that the US is preparing for a fully-fledged assault on the city.
Previous deals in Falluja, notably a ceasefire, have broken down and heavy US air strikes this week combined with tough talk by US President George Bush seemed to herald a possible all-out assault.
Thousands of locals have been
trying to flee the fighting
But marines and police said troops would now start withdrawing from their siege lines.
A field commander said troops would start withdrawing from the industrial area in south Falluja on Friday to allow for a transfer of security to take place.
Lieutenant-Colonel Brennan Byrn said that soldiers of the fifth battalion would return to their base outside Falluja after the handover of responsibility to Iraqi authorities.
He added that the marines would withdraw from the northern outskirts of the city on 2 May in order to open roads from the north and allow for Iraqi patrols to move into Falluja by 10 May.
But Falluja police chief Sabar al-Janabi said the withdrawal would be completed by 30 April. He said US officers seemed to have backed away from insistence on conducting joint patrols with Iraqi forces in the city.
Thousands of people have fled Falluja, where doctors say some 600 people died during the first US offensive three weeks ago in response to the killing of four American security guards.
A Reuters journalist watched US marines open fire on a minibus at a checkpoint on the outskirts, setting the vehicle ablaze. Up to four civilians died, a policeman said.
On one of the bloodiest days of the bloodiest month for US troops in Iraq - 10 soldiers were killed, including eight by a car bomb - any progress towards a peaceful settlement would be welcome news in Washington.
US has used AC-130H warplanes
to strike Falluja
That took to at least 125 the number of US soldiers killed in action this month, far outnumbering the toll in the three weeks it took to dash to Baghdad and topple Saddam a year ago. In all, 534 have been killed since the invasion of Iraq in March 2003.
Faced with such violence and armed defiance in two key towns, Bush had given commanders a free hand.
"Our military commanders will take whatever actions necessary to secure Falluja," he said.
But United Nations Secretary-General Kofi Annan has appealed to Bush to show restraint, saying bloodshed could turn Iraqis against the occupying forces even as the UN works with Washington to restore an Iraqi government on 30 June.
In other violence on Thursday, a South African civilian was killed in a drive-by shooting near oil company offices in the southern city of Basra. The head of security for the vital northern oilfields was wounded in Kirkuk.