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A French warplane has destroyed a Libyan aircraft that had been flying in breach of the UN no-fly zone, French officials say.
The smaller trainer aircraft had just landed in the besieged city of Misrata when it was attacked, they say.
It is the first incident of its kind since enforcement of the zone began.
Meanwhile, Turkey's foreign minister has said Nato will take command of the international mission in Libya within a day or two.
"Compromise has been reached in principle in a very short time," Ahmet Davutoglu was quoted as saying after a conference call with his US, French and British counterparts.
Turkey, a Nato member, had earlier raised objections to the organisation taking command without certain conditions first being agreed.
Reports from Brussels suggest that the mission might be placed under Nato control, but overseen by a military council including some Arab states.
A senior US military official confirmed the handover could come as early as this weekend.
Vice-Admiral Bill Gortney also told a Pentagon briefing that a total of 350 aircraft were now involved in the operation in some way, about half of them American.
A total of 38 ships were participating, he said, 12 of them from the US.
He insisted that Libyan ground forces would continue to be attacked as long as they threatened the lives of civilians.
"Our message to the regime troops is simple - stop fighting... stop obeying Gaddafi's orders," he said.
UN Secretary General Ban Ki-moon has said there is no sign that the Libyan government is meeting demands for an immediate ceasefire.
He warned that the UN Security Council would take "additional measures" if Libya did not comply.
A sixth consecutive night of bombing was reported to be under way on Thursday, with Libyan state television reporting that areas in Tripoli and Tajoura had been hit.
Dozens of coalition missiles have already hit military bases, with the aim of ending Col Muammar Gaddafi's ability to launch air attacks.
UK officials said on Wednesday that Libya's air force no longer existed as a fighting force.
Initial reports of the French action said the Libyan plane, a G-2/Galeb with a single engine, was in the air when it was hit.
But French military spokesman Col Thierry Burkhard later said the plane had just landed when the attack took place.
The French jet, a Rafale, fired an air-to-ground missile, other reports said.
Earlier, the French military said their planes had hit an air base about 250km (155 miles) south of the Libyan coastline, but did not give any further information on the location of the target or the damage.
Western military planes were also said to have hit the town of Sebha in southern Libya, according to residents and media reports.
Fresh fighting has meanwhile been reported in Misrata, scene of a bitter battle for control which has lasted for many days.
One doctor quoted by the AFP news agency said pro-Gaddafi forces had killed more than 100 people and injured 1,300 in the past week.
Further east in the strategically important city of Ajdabiya, residents described shelling, gunfire and houses on fire. One report said rebels were moving closer to the city but remained out-gunned by pro-Gaddafi forces.
In the main eastern city of Benghazi, rebel spokesman Mustafa Gheriani told the BBC that 17,000 fighters had set out from the city to join the battle to the west.
Although he admitted that the rebel forces were on a "learning curve", he insisted that they all knew how to operate their weapons and were committed.
"We will slowly advance," he said. "[Gaddafi's forces] have no reason to fight, no cause, while we do.
"We have given so much blood and we're willing to give some more if we have to."
The International Criminal Court's prosecutor, Luis Moreno-Ocampo, has said he is "100% certain" that charges of crimes against humanity will be brought against Col Gaddafi's regime.
An initial inquiry should end in May, he said, and a second case might follow to investigate more recent attacks on civilians.
Earlier this week Nato members had been holding talks about assuming responsibility for the no-fly zone over Libya, without agreement.
The US was keen to relinquish control, but there were disagreements about who should take on the role, and what the exact terms of engagement would be.
Turkey said it wanted any Nato-led action to focus directly on enforcing the no-fly zone and arms embargo, rather than allowing any continuing strikes against ground forces.
The Turkish parliament has backed a government decision to join the blockade. Four frigates, a submarine and a support vessel are being provided by Turkey.
In a separate development, African Union chairman Jean Ping has invited members of the Libyan government and opposition to talks in Ethiopia.
Representatives of the European Union, the UN Security Council and neighbouring countries have also been invited to the talks, scheduled to be held in Addis Ababa on Friday.
The UK has invited fellow Nato members, the UN, Arab League and African Union, and a number of Arab nations, to a conference in London on Tuesday.