The New York Times reported black smoke from an oil fire over the town and large explosions of uncertain origin.
The rebels earlier Monday entered the town's northeast and took the New Brega district.
Libyan leader Moammar Gadhafi forces were still holding the local university, and oil facilities sustained steady rebel machine gun and rocket fire, backed by a possible NATO airstrike, the Times said.
The BBC reported the rebels seemed more organized and disciplined than before but are still poorly equipped and trained.
A rebel spokesman rejected any transition of power involving any of Gadhafi's sons, the BBC said.
The spokesman said the Transitional National Council in Benghazi opposed the idea -- reported by several media outlets -- that Saif and Saadi Gadhafi could step in as interim leaders if their father resigned.
Gadhafi's deputy foreign minister, Abdul Ati al-Obeidi, who flew to Athens Sunday, told Greek officials the dictator wants to end the fighting, the BBC said.
"From the Libyan envoy's comments it appears that the regime is seeking a solution," Greek Foreign Minister Dimitris Droutsas said.