The commander of Libya's rebel forces has said Nato apologised for mistakenly hitting a column of rebel tanks near the eastern town of Ajdabiya.
Gen Abdelfatah Yunis said the deadly air strike had occurred despite a warning to Nato that the tanks were being moved to the front line.
Nato said it was investigating the claim, without giving further details.
Rebels said four rebels died, while local doctors told the BBC at least 13 fighters had been killed in the strike.
"We would like to receive answers about what happened. We would like a rational and convincing explanation," Gen Yunis said.
He also said such mistakes must not be repeated and called for better co-operation in the future.
But the general stressed that there was no tension between the opposition and Nato, despite anger among some local residents.
It was the third such incident in recent days involving international forces deployed to protect Libyan civilians.
The BBC's Wyre Davies reported chaotic scenes on the outskirts of Ajdabiya, with rebel forces in retreat.
Meanwhile, a relief ship carrying emergency supplies of food and medicine has arrived in the besieged rebel-held city of Misrata, in western Libya.
The rebels hit in the air strike had been moving a group of tanks, armoured vehicles and rocket launchers near the front line between the towns of Ajdabiya and Brega in more than 30 transporters.
One rebel commander told the BBC he saw at least four missiles land among rebel fighters.
As well as those killed, many more were injured, he said.
There is considerable anger among rebel troops at what appears to have been a terrible mistake, our correspondent says.
They are asking why rebel units were hit, he adds, when they could be seen clearly advancing in a westerly direction towards the front line.
"It is unbelievable," said one Benghazi resident. "Nato, with all the equipment they have - is this the second mistake? Is it really a mistake or something arranged secretly?"
Another said: "The allies and the UN Security Council must allow us to be armed. We don't want anything, just to be armed to defend ourselves against this dictator and fascist."
Rebel forces in the area began retreating on Wednesday after heavy bombardment from government forces.
They had been calling for more Nato air strikes in recent days.
Nato said it was investigating the incident, noting that the area where the attack occurred was "unclear and fluid with mechanised weapons travelling in all directions".
"What remains clear is that Nato will continue to uphold the UN mandate and strike forces that can potentially cause harm to the civilian population of Libya," said the alliance in a statement.
Meanwhile, a different rebel spokesman said Thursday's fatal air strike was carried out by pro-government forces rather than by Nato.
"This was not a Nato air-strike; on the contrary, it was conducted by Gaddafi's brigades using SIAI Marchetti SF-260 planes," Col Ahmad Bani told al-Arabiya television.
The alliance took over air operations from a US, French and British coalition a week ago, to enforce a UN mandate to protect civilians in Libya.
Last Friday, at least 13 people were reportedly killed when a coalition plane fired on a rebel convoy between Brega and Ajdabiya.
Three medical students were among the dead.
The attack came after rebels reportedly fired an anti-aircraft gun.
In a separate incident, seven civilians died and 25 were hurt in a coalition air strike on a pro-Gaddafi convoy near Brega.
Further west, in Libya's third-biggest city, Misrata, a ship chartered by the UN World Food Programme delivered hundreds of tonnes of high energy biscuits, flour, and water purification tablets, as well as enough medicine to last 30,000 people for a month.
Misrata has been under attack by Libyan government forces for several weeks, and Libyan rebels have complained it would "cease to exist" within a week unless Nato took action to save it.