Government forces are undertaking a twin-pronged assault on rebel positions in east and west Libya.
Government soldiers have surrounded and made their first ground assault on Ajdabiya - the last town before the main rebel-held city of Benghazi.
Tanks are also pounding the last rebel-controlled city in the west, Misrata.
Meanwhile, French President Nicolas Sarkozy has urged the UN Security Council to back a draft resolution that would include a military no-fly zone.
In a letter to member states, Mr Sarkozy said Col Muammar Gaddafi had continued his "murderous actions against his people" despite a resolution last month, and that they now had to "assume their responsibilities".
"Let's save the martyred Libyan people together. Time is now counted in days, or even hours. The worst would be for the Arab League's call and the Security Council's decisions to fail because of armed force."
The UK has also expressed its support for the resolution drafted by Lebanon, which authorises member states "to take all necessary measures to enforce compliance" by the Libyan authorities.
UN Secretary General Ban Ki-moon has called for a ceasefire.
Meanwhile, the US Secretary of State, Hillary Clinton, told the BBC in Cairo that the Libyan leader seemed "determined to turn the clock back" and kill as many civilians as possible.
The BBC's Jon Leyne Benghazi says forces loyal to Col Gaddafi have now taken up positions outside Ajdabiya, only 160km (100 miles) away from the rebel stronghold of Benghazi, where a million people live.
Tanks, artillery and warplanes have been bombarding the town, but the latest reports are that opposition forces inside are holding out.
Abdul Karim Mohammed, a local doctor, told the AFP news agency that at least 26 people, mostly civilians, had been killed since Tuesday.
Jamal Mansour, a rebel commander, said: "There's heavy fighting around Ajdabiya, they're carrying out a scorched-earth policy."
"There's heavy, sustained tank shelling and earlier there were air strikes, but now the revolutionaries managed to take seven tanks from those dogs and, God willing, we will succeed."
Mr Mansour said the rebels still controlled the roads to Benghazi and Tobruk.
Despite Libyan state television reports on Tuesday that Adjdabiya was "totally controlled and is being cleansed of armed gangs", eyewitness reports suggested that fighting was continuing in the town on Wednesday afternoon,
AP reporters travelling with government forces said charred and bullet-ridden vehicles littered the side of the road from Brega, to the south. They also saw several bodies. Their convoy did not enter Ajdabiya because the commander said there were still "pockets of resistance".
Meanwhile, the New York Times has said four of its journalists who were reporting from Ajdabiya have gone missing, saying it had received reports they had been "swept up by Libyan government forces".
Executive editor Bill Keller said he had not been able to confirm the information, adding that Libyan government officials had told him they were attempting to ascertain the whereabouts of the journalists.
UN decision 'soon'
In Misrata, Libya's third city, rebels said they had managed to hold off government troops who had attacked with tanks and artillery.
Saadoun al-Misrati, a rebel spokesman, told BBC Arabic that Gaddafi loyalists had been firing artillery and machine-guns at the city's entrances.
He added that the city was in urgent need of medical supplies, but that basic foodstuffs were still available.
Al-Jazeera cited rebels in Misrata as saying 11 people had been killed on Wednesday, while a witness said mosques and homes had been bombed.
There is no independent way of verifying these details.
Our correspondent says the situation in Benghazi is getting more tense by the hour, and the calls for a no-fly zone more desperate.
Jalal al-Gallal of the Transitional National Council said there would be a "massacre" if the international community did not intervene.
"He [Gaddafi] will kill civilians, he will kill dreams, he will destroy us," he told the BBC. "It will be on the international community's conscience."
Countries such as Russia, China and Germany are understood to harbour doubts about military intervention in Libya.
The Arab League has backed the idea but Tuesday's meeting of G8 foreign ministers in Paris failed to do so.
Hillary Clinton said she was confident a decision would be made very soon by the international community to protect the Libyan people. She said authorisation through the UN Security Council was key, and insisted there should be Arab participation and leadership in any action.
"Many different actions are being considered," she added. "Yes, a no-fly zone, but others as well to enable the protection of Libyan citizens against their own leader, who seems determined to turn the clock back and kill as many of them as possible."
Asked about targeted strikes, she said all options were on the table.
Aid agencies withdraw
One of Col Gaddafi's sons, Saif al-Islam, has claimed Benghazi will be recaptured soon even if a no-fly zone is imposed.
"Everything will be over in 48 hours," he told Euronews.
But the government probably does not have the forces yet to launch a frontal assault let alone to take the city in such a short time, correspondents say.
Nevertheless, the International Committee of the Red Cross (ICRC) has said it has withdrawn its staff from Benghazi due to the fighting and moved them to Tobruk, further to the east.
"We are extremely concerned about what will happen to civilians, the sick and wounded, detainees and others who are entitled to protection in times of conflict," said Simon Brooks, head of the ICRC mission in Libya.
Humanitarian activities will still be carried out by the Libyan Red Crescent.
The medical aid agency Medecins Sans Frontieres (MSF) also announced earlier on Wednesday that it was pulling out of Benghazi.
"Conditions have made it effectively impossible for medical teams to travel safely to areas where the fighting has created the greatest needs."