Aid staff are battling to cope with an exodus that has seen some 140,000 people crossing into Tunisia and Egypt.
The UN has suspended Libya from its Human Rights Council and has called for a mass humanitarian evacuation.
Libyan leader Col Muammar Gaddafi has played down protests and is trying to regain control of areas in the west.
He is facing a massive challenge to his 41-year rule, with protesters in control of towns in eastern Libya.
Witnesses said pro-Gaddafi forces tried to retake the western cities of Zawiya, Misrata and Nalut on Monday but were repulsed by rebels helped by defecting army units.
There are fears in Zawiya that the city may be attacked from the air, but the rebels remained defiant.
“We’re not here for power, authority or money,” they said in a message aimed at Col Gaddafi.
“We are here for the cause of freedom and the price we are willing to pay is with our own blood. It’s victory or death.”
Protesters holding Nalut and the town of Zintan, 145km (70 miles) south-west of Tripoli, both reported the approach of Gaddafi forces and said they feared fresh attacks.
BBC, Jim Muir
