Sunday's strike was the latest of a series of attacks on buildings the Americans allege were sheltering "guerrillas" and "foreign militants".
Doctor Ahmad Ghanim said earlier in the day that 11 bodies had been brought to Falluja general hospital after the bombing in the south-east of the city, which reduced the house to rubble.
The US-led military said the attack was directed at a den of about 25 people with suspected links to resistance fighter Abu Musab al-Zarqawi.
"The strike, conducted at 2:03am (2203 GMT on Saturday) ... destroyed defensive fighting positions and trench lines near the remains of a house and a foreign fighter checkpoint," said Brigadier General Erv Lessel, the deputy director for the occupation force in Iraq.
US's 'prime enemy'
About 25 people suspected of having ties with the Jordanian-born fighter were at the site just before the attack was launched, Lessel said in a statement, describing it as a "precision operation" based on US and Iraqi intelligence sources.
The US Marine Corps pulled out of the rebellious city west of Baghdad after weeks of fierce fighting in April that killed hundreds of Iraqis. Critics of the withdrawal say the city has since become a haven for resistance fighters.
Iraqis say they have not seen
any sign of al-Zarqawi in Falluja
Several times over the past two months the US military has launched air strikes on buildings in Falluja which it says are safe houses for fighters loyal to Abu Musab al-Zarqawi, a Jordanian accused of masterminding a series of attacks.
Washington calls al-Zarqawi, who it says has links to al-Qaida, its prime enemy in Iraq and has put a $25 million price on his head.
Iraqi Prime Minister Iyad Allawi said on Sunday he gave the US military the green light for the attack.
Republican Guard leader
"Yesterday the multinational force asked Prime Minister Allawi for permission to make an accurate operation against some definite places ... Places where terrorists hide out," said an official from the prime minister's office.
Meanwhile, a senior Iraqi leader in Saddam Hussein's elite Republican Guard has been captured near Tikrit, a US military spokesman said on Sunday.
"Yesterday the multinational force asked Prime Minister Allawi for permission to make an accurate operation against some definite places ... Places where terrorists hide out"
Statement from Iyad Allawi's office
US major Neal O'Brien said US-led forces captured Sufian Mahir Hasan, a former major general in the Republican Guard, near Tikrit on 16 July.
"He is suspected of planning and financing attacks against the Iraqi people, Iraqi security forces and multinational forces," O'Brien said.