They are also pushing forward in the western Nafusa mountains against Qadhafi's forces, which a top Nato commander said were no longer able to launch a credible military offensive.
The rebels, who, inspired by revolts in Egypt and Tunisia, launched popular protests against Qadhafi on February 17, vowed that in just a few days they plan to retake the strategic oil hub of Brega, nestled on the Gulf of Syrte.
Rebels, backed by Nato helicopters, have tried for the past three weeks to seize the vital port 240 kilometres (140 miles) southwest of their eastern stronghold Benghazi.
On Wednesday, they were poised on the eastern fringes of the city, the outskirts of its residential area, an AFP journalist saw.
By late Thursday, after a day of fighting, the rebels said they had taken control of “residential zone number three,” one of the three in Brega.
“Every day, we are gaining ground. We are at the entrance of the city. Some of our fighters have even got inside the residential area,” said Fawzi Bukatif, a civil engineer who became a top commander of the insurrection.
Their counterparts in the western city of Misrata, meanwhile, have gone on the offensive against Qadhafi's troops in the town of Tuarga in an effort to end the barrage of missiles that hits their home town almost daily.
Commanders and fighters told AFP the rebels had pushed into the centre of Tuarga, around 40 kilometres (25 miles) south of Misrata on Thursday.
“They are firing rockets into Misrata every day,” said Tariq, a 26-year-old fighter who had pulled a few kilometres back from the front to fix his truck-mounted rocket launcher.
“Today is the day we stop them; today we moved inside Tuarga.”
Nato had softened the ground for the rebels overnight on Wednesday, hitting three command and control nodes and two military storage facilities in Tuarga.
After that starting gun Hajj Ali, commander of the Taliq Freedom Brigade - which in earlier battles stopped Qadhafi forces reaching Misrata's port - said rebel forces were moving into the centre of Tuarga in a pincer from the west and east.
The rebels hope to cut of supply lines to the town and disrupt rocket positions, but Ali said they were moving cautiously.
“We have to be careful. It does not look like they have hostages, but there are a lot of snipers,” he said.
In Misrata, on Thursday evening, there were scenes of jubilation amid news that the offensive had been successful in reaching the town.
Car horns blared and tracer fire was shot into the air in celebration.
But rebel officials admitted there was still some fighting to do.
Nato was authorised in March by UN Security Council resolution 1973 to defend Libya's civilian population from attacks by Colonel Qadhafi's regime, which faces a popular revolt after 42 years in power.
The alliance's top Libya commander, Canada's Lieutenant-General Charles Bouchard, told AFP the air strikes had affected Qadhafi's military capabilities.
“The Qadhafi regime's forces continue to be weakened, both in strength and their will to fight,” he said, speaking from his Italy headquarters.
“They are no longer able to launch a credible offensive,” he added.
Today, there's “activity” on three fronts, in Brega, in Misrata and the Nafusa mountains, Bouchard said, adding that Qadhafi's forces are “shooting blindly on civilians.”
“On the three fronts, we're seeing changes as anti-Qadhafi forces march forward to stop the attacks on the population,” he added.
Qadhafi's regime last week accused Nato of killing 85 people, including women and children, with airstrikes on the village of Majer, south of the disputed city of Zliten, charges denied by Bouchard.
“I can assure you that the target was a legitimate one that contained mercenaries, a command center and 4x4 vehicles modified with automatic weapons, rocket launchers or mortars,” Bouchard said.
“I cannot believe that 85 civilians were present when we struck in the wee hours of the morning, and given our intelligence” on the target, he added.
“I can assure you that there (were not) 85 civilians present, but I cannot assure you that there were none at all.”
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