The Pentagon expects to hand over control of allied military operations in Libya “in a matter of days”, either to a UK-France coalition or to Nato, US Defence Secretary Robert Gates says.
Meanwhile, witnesses in Tripoli reported hearing loud blasts and anti-aircraft fire on Sunday night.
Smoke rose from near the compound of Libyan leader Col Muammar Gaddafi.
French planes patrolled over Libya on Sunday, but the Pentagon said Libya’s air defences were effectively degraded.
While the US will continue to play a part in military operations, Mr Gates says it “will not have the pre-eminent role.”
“I think there is a sensitivity on the part of the Arab League to being seen to be operating under a Nato umbrella,” Mr Gates said. “And so the question is if there is a way we can work out Nato’s command and control machinery without it being a Nato mission and without a Nato flag, and so on.”
Mr Gates also said a break-up of Libya would be a formula for instability. The east of the country, where the month-old revolt began, has historically been much more opposed to Col Gaddafi’s rule, while the west and the area around Tripoli constitute his heartland.
Plume of smoke
A BBC reporter in Tripoli says a heavy barrage of anti-aircraft fire was heard in the city centre on Sunday night.
A column of smoke rose in the area of Bab al-Aziziya, where Col Gaddafi has his military base and compound, our reporter says.
However, he adds that it is believed there are anti-aircraft weapons close to Bab al-Aziziya, which may well have been targeted, rather than the compound itself.
Meanwhile, heavy gunfire and sporadic explosions were heard in the streets of the rebel stronghold of Benghazi on Sunday night, a witness told Reuters.
There were also unconfirmed reports of pro-Gaddafi fighters opening fire from cars in the city.
In a statement from the Pentagon on Sunday, US Vice Adm William Gortney said coalition raids were “judged to have been very effective” and no new Libyan air activity had been reported.
“Benghazi is not completely safe from attack but it is certainly under less threat than it was yesterday,” he said.
Meanwhile, the build-up of forces to enforce the no-fly zone continues.
Qatar is to send four planes to join the coalition enforcing the UN-mandated no-fly zone, the US and France have said.
The move would make Qatar the first Arab country to play an active part in the campaign against Col Gaddafi, who has been battling a month-long revolt.
Other Arab countries are also preparing to join the campaign against Col Gaddafi, Vice Adm Gortley said, adding that those governments would make their own announcements in due course.
The French aircraft carrier Charles de Gaulle has left the Mediterranean port of Toulon for Libya, while Denmark and Norway are each sending six planes. Spain has sent at least three planes, plus a refuelling aircraft, while Italy also has jets ready to deploy.
The head of the Arab League, who supported the idea of a no-fly zone, has criticised the severity of the bombardment.
“What is happening in Libya differs from the aim of imposing a no-fly zone, and what we want is the protection of civilians and not the bombardment of more civilians,” said Arab League Secretary General Amr Moussa.
Arab League support was a key factor in getting UN Security Council backing for the resolution authorising the move.
In a news conference on Sunday, a Libyan military spokesman said its armed forces had ordered a ceasefire across the entire country, beginning at 2100 local time (1900 GMT).
However, the BBC’s Allan Little in Tripoli says the government had been insisting that its troops were already observing a ceasefire order made on Friday.
Despite Friday’s announcement, our correspondent adds, pro-Gaddafi troops have tried to enter Benghazi and have been in action at Misrata.
A rebel spokesman in Misrata told the BBC that pro-Gaddafi forces had launched fresh attacks on Sunday with heavy shelling.
Col Gaddafi has ruled Libya for more than 40 years. An uprising against him began last month after the long-time leaders of neighbouring Tunisia and Egypt were toppled.