Forces loyal to Libyan leader Muammar Gaddafi have launched an attack on Misrata, the last city still in opposition hands in the west of the country.
Witnesses say tanks and artillery bombarded Misrata from early morning.
Rebels say they have managed to hold off the troops.
Government soldiers have also surrounded and made their first ground assault on Ajdabiya, the BBC reports.
Ajdabiya is the last town before the main rebel-held city of Benghazi.
The United Nations Security Council remains split over a draft resolution authorising a no-fly zone over Libya to stop the bombing of civilians.
A closed session of the council is under way in New York.
French President Nicolas Sarkozy has called on the council to endorse a draft resolution authorising the no-fly zone.
British Foreign Secretary William Hague has said Britain could use an existing doctrine to help impose a zone without a fresh UN resolution.