The Associated Press revelation will add further fuel for critics who say US forces acted illegally in killing the unarmed Saudi fugitive. The Obama administration insists the shooting was lawful.
Meanwhile, US relations with Pakistan, already at their lowest point in a decade, have found a fresh point of friction following an exchange of fire between Nato and Pakistani forces along the Afghan border.
Two Pakistani soldiers were injured after opening fire on two Nato helicopters that crossed into Datta Khel, North Waziristan.
Pakistan's military, already livid over the Bin Laden raid, condemned the incident as a "violation of Pakistan air space" and lodged a "strong protest". A Nato spokesman in Kabul said the shooting started after a Nato base came under fire from the Pakistani side of the border.
The AP account, based on interviews with senior US officials, resolves some subsidiary mysteries about the size and sequencing of the dramatic US Navy Seal raid that ended the world's largest manhunt on 2 May. But it also throws up fresh questions about how Pakistan's air defence systems failed to stop the American forces entering – or leaving.
The US raiding party slipped into Pakistan on five helicopters – two stealth Black Hawks carrying 23 Navy Seals, an interpreter and a sniffer dog named Cairo, and three Chinooks carrying 24 backup soldiers that landed in a remote mountain area north of Abbottabad, the garrison town where Bin Laden was hiding.
In recent days, two Pakistani television channels have identified the mountain area as Khala Dhaka, a semi-autonomous tribal area, interviewing villagers who saw the US craft landing and taking off.
The Black Hawks that swooped on Bin Laden's compound were equipped with special technology to muffle the tail rotor and engine noise, the AP reported. Some experts have speculated it was also equipped with a special skin to fool radar. The soldiers planned to swoop on Bin Laden's house from three sides: sliding down ropes onto the roof, the compound and outside the wall.
But the first Black Hawk swayed erratically as it hovered over the compound owing to higher than expected temperatures and crashed against a wall, irreparably damaging its tail. The pilot ditched the plane in Bin Laden's yard and the entire raiding party entered from the ground floor, using small explosives to blow their way through walls and doors.
The AP reported that the Americans found "barriers" at each stair landing of the three-storey building, encountered fire once and killed three men and one woman. The account did not specify how many of the dead were armed.
After 15 minutes the Seals, passing huddles of frightened children, reached the top floor where they found Bin Laden at the end of the hallway. They said they recognised him "immediately". Bin Laden ducked into a room, followed quickly by three Seals.
The first soldier pushed aside two women who tried to protect Bin Laden, apparently fearing they were wearing suicide vests, while the second opened fire on the al-Qaida leader, hitting him in the head and chest.
Moments later, as the Americans photographed his body, they found an AK-47 rifle and a Makarov pistol on a shelf beside the door they had just entered. Bin Laden had not touched the weapons, according to the AP account.
Just over 20 minutes later a Chinook helicopter arrived to collect Bin Laden's body, a trove of computer disks, and the soldiers whose helicopter had crashed, now destroyed except for the rear rotor and tail.
Controversy over the manner of Bin Laden's death has dogged the White House since 2 May, especially after early claims that Bin Laden had been armed and used one of his wives as a human shield proved to be false.
The only witnesses who could contradict the American account are Bin Laden's three wives and children, who are currently in Pakistani custody. After much pressure from Washington, US officials were allowed to briefly speak with them last week. The women reportedly refused to answer questions and Pakistan says they will be repatriated to their native Saudi Arabia and Yemen. It is not clear when this will happen.
The AP also reported that there had been four previous special forces incursions into Pakistan, echoing a December 2009 report in the Guardian. A senior Nato official said two of the clandestine raids targeted "high-value targets", while a third was to recover a crashed Predator drone.
The account comes a day after a visit by Senator John Kerry, who was in the capital, Islamabad, yesterday to try and "reset" the fragile alliance, claiming that Pakistan was not informed in advance for operational reasons and not due to any distrust of the Pakistanis.
A similar issue has arisen from the Bin Laden raid. Kerry, after intensive meetings with Pakistani military chiefs, said he had secured a promise that the rear rotor of the Black Hawk would be returned to US custody, amid US fears it would be passed to China and reverse-engineered.
Pakistan's leadership has moved closer to its decades-old ally China. The prime minister, Yousaf Raza Gilani, today embarked on a four-day visit to China, a country he pointedly described as "our best and most trusted friend".