Nato's Secretary General, Anders Fogh Rasmussen, has said it has decided to take on the whole military operation in Libya "with immediate effect".
The alliance will enforce "all aspects" of the UN resolution authorising action to protect civilians. "Nothing more, nothing less," Mr Rasmussen added.
Libyan rebels have been advancing westwards, capturing towns abandoned by Col Muammar Gaddafi's forces.
Explosions were also heard in Sirte and the capital, Tripoli, on Sunday night.
It is not clear what the causes of the blasts were, though state TV said the cities were being bombed by "Crusader and colonialist" forces. A government spokesman also said the town of Sabha had been targeted.
Sirte, the Libyan leader's stronghold, is only 100km (60 miles) west of the town of Nufaila, which rebel forces said they had reached. Foreign journalists said the city was swarming with soldiers on patrol.
The rebels earlier retook the eastern coastal towns of Ras Lanuf, Brega, Uqayla and Bin Jawad, only a day after seizing control of Ajdabiya.
Nato's plan to take responsibility for operations in Libya had already been agreed by military representatives of the 28 member states, but it needed ambassadors to provide political approval at a meeting in Brussels.