Nato has admitted "a weapons systems failure" may have led to civilian casualties in Sunday morning's air strike in the Libyan capital, Tripoli.
The alliance said the intended target was a missile site, but "it appears that one weapon" did not hit it.
The Libyan government earlier said Nato had bombed a residential area, killing nine civilians, including two babies.
Meanwhile, rebel leaders said their administration had run out of money as donors' pledges had not materialised.
They told a news conference in the eastern city of Benghazi that they were still waiting for funds that should have been deposited by last week.
Nato is enforcing a UN resolution to protect civilians in Libya.
But on Sunday evening, the commander of operation Unified Protector, Lt Gen Charles Bouchard, said: "Nato regrets the loss of innocent civilian lives and takes great care in conducting strikes against a regime determined to use violence against its own citizens.
"Although we are still determining the specifics of this event, indications are that a weapons system failure may have caused this incident."
The statement said that more than 11,500 sorties had already been conducted and "every mission is planned and executed with tremendous care to avoid civilian casualties".
Nato later released a video statement.
The BBC's Jeremy Bowen in Tripoli says the incident could prompt questions about what Nato is achieving in Libya - not least by Nato members who never agreed with the operation.
Sunday's attack, in one of the capital's poorer neighbourhoods, happened shortly after midnight, Libyan officials say.
They say that nine people were killed, including two babies, and another 18 people injured. It is not possible to verify this claim independently.
Our correspondent, who was taken to the site by government officials, saw two bodies being removed from the rubble.
Scores of men were working alongside the emergency services, pulling at sections of rubble and looking for bodies.
Our correspondent was then taken to a Tripoli hospital where he was shown the bodies of two men, a woman and two babies, who government officials said had been killed in the strike.
Rapidly shifting lines
Libyan Deputy Foreign Minister Khaled Kaim said the incident represented a "deliberate targeting of civilian houses".
The incident came shortly after Nato "regretted any possible loss of life" from an accidental air strike on a rebel column near the oil refinery town of Brega on Thursday.
A rebel spokesman said it was to Nato's credit that it had admitted that mistake.
Nato's mission - to enforce a no-fly zone over Libya to protect civilians using "all necessary measures" short of a ground invasion - began in March in response to Col Muammar Gaddafi's violent response to a popular uprising.
The intervention was mandated by the UN, and led by France, Britain and the US until the end of March, when Nato took over.
Having initially been given 90 days - which would have run out on 27 June - the mission has been extended for a further 90 days.
The rebels control a third of Libya in the east and pockets in the west, including Misrata, although Tripoli remains under government control.
On Sunday, senior officials from the rebel Transitional National Council (TNC) issued an urgent plea for foreign financial aid.
Despite having won promises of assistance from their Western and Arab supporters, they have yet to receive any money, they said.
They believe they need more than $3bn (£1.9bn) to cover salaries and other needs in the next six months.
So far the TNC has paid salaries and met other costs by drawing on whatever money was left in the Benghazi branch of Libya's central bank.
But now those coffers are empty, rebel strategic adviser Shamsuddin Abdul Mullah told the BBC's Bridget Kendall in Benghazi.
Mr Abdul Mullah said they still hoped the delay was temporary, but that it was becoming increasingly hard to explain.
Cash was needed urgently to buy medical supplies for the frontline, as well as to avoid popular frustration with a situation that was becoming increasingly dire, he added.