Col Muammar Gaddafi's forces are slowly pushing towards the main rebel-held towns in Libya, reports say.
Ajdabiya, the last major town before the rebel base in Benghazi, came under heavy aerial attack. In the west, ground forces and tanks have begun shelling the town of Zuwara.
Rebels say they have retaken Brega, but the government has denied the claim.
Earlier, the UN Security Council met to discuss the imposition of a no-fly zone, but there was no consensus.
The BBC's Barbara Plett says there were divisions about authorising such a zone, with France calling it a game-changer, but countries such as Russia expressed caution, saying serious questions remained.
Meanwhile, a UN envoy, Abdul Ilah Khatib, has met Libyan Foreign Minister Moussa Kusa in Tripoli.
In the meeting, Mr Khatib, a former Jordanian foreign minister, reiterated demands for an end to the violence and requested access for humanitarian groups, a UN spokesman said.
With fighting continuing in the east of Libya, it is not clear exactly where the front line is.
The eastern oil town of Brega changed hands several times over the weekend, amid a relentless barrage of air and ground attacks by government forces.
Rebel forces said on Monday that they had retaken the town, capturing a number of elite government troops and killing others. The statement has not been independently confirmed.
In western Libya, a government assault on the rebel-held city of Misrata seems to have stalled, says the BBC's Jon Leyne from the rebel stronghold of Benghazi.
Misrata, some 200km (130 miles) east of the capital, is the only major city held by insurgents outside the east of the country.
According to rebel leaders, fighting has broken out amongst government army units, some of whom do not want to attack Libyan civilians.
Col Gaddafi's forces have meanwhile entered the opposition held town of Zuwara, west of the city of Zawiya which they retook last week, according to Reuters news agency.
"I can see the tanks from where I am now and they are around 500 meters from the centre of Zuwara," Tarek Abdullah, a resident, told Reuters.
"There are still clashes but I think soon the whole town will fall into their hands," he said.
Other residents have reported intensified shelling which sent people running from their houses, afraid of being hit.
Libyan army spokesman Col Milad Hussein said in Tripoli that government troops were "marching to cleanse the country" of insurgents, whom he called "rats and terrorists."
East of Brega, and beyond rebel lines, pro-Gaddafi planes bombed the town of Ajdabiya, rebels said. Ajdabiya is the last big population centre before the main rebel city, Benghazi.
The rebel's top commander, former interior minister Gen Abdel Fatah Younis, said that the war was entering a crucial phase.
"The battle for Ajdabiya is very important for us," he told a news conference in Benghazi on Sunday. "We feel that the enemy will have serious logistical problems in supplying their troops," he added.
'Dragged into war'
As the fighting gets closer to the major city of Benghazi, there is the potential for many more civilian casualties, particularly if Col Gaddafi's aircraft can operate unchecked, our correspondent says.
The policy would be aimed at preventing Col Gaddafi's forces using warplanes to attack rebel positions, although no clear position has emerged on exactly how this would be achieved.
The Arab League threw its support behind the proposal on Saturday, but Nato and the US have so far appeared reluctant about any direct military involvement in the conflict.
Our correspondent says that several countries remained cautious about the prospect at the UN Security Council meeting on Monday.
Diplomats said these included not only Russia and China, who traditionally oppose international intervention, but also the US, Germany, South Africa and Brazil, our correspondent says.
After Monday's meeting, Russian UN envoy Vitaly Churkin said that questions remained about a no-fly zone, but indicated that Moscow was not ruling out the proposal.
Foreign ministers of the G8 group of nations have meanwhile been meeting in Paris.
German foreign minister, Guido Westerwelle, said a no-fly zone would constitute military intervention and that Germany did not want to get dragged into a war.
Meanwhile, EU's foreign affairs chief Catherine Ashton has said a mission has been sent to rebel-held Benghazi to gather information and assess the situation.
British Prime Minister David Cameron continued to press for action, saying Col Gaddafi should not be allowed to continue "brutalising his own people".
In a statement to the British House of Commons, he did not rule out the possibility of arming the Libyan rebels - although he acknowledged that there were difficulties, including the continuing UN arms embargo.
Nato has previously cited regional and international support for the idea as a key condition before any intervention could possibly go ahead.
Turkey, the only Muslim member of Nato, has strongly opposed the idea, warning it could create "dangerous results".