The rebels said they were making a push for the country's capital, the BBC reported Monday.
The rebel spokesman in the Nafsua Mountains reported heavy fighting near the town of Bir al-Ghanam.
The International Criminal Court decided Monday to issue an arrest warrant for Gadhafi.
ICC Prosecutor Luis Moreno-Ocampo said he has evidence tying Gadhafi, his son, Saif, and brother-in-law Abdullah al-Sanussi, head of Libya's intelligence agency, to crimes against humanity in their attempt to quell opponents fighting to oust Gadhafi for months.
The son is Saif al-Islam Gadhafi. Another son named Saif (Saif al-Arab Gadhafi) was killed in an airstrike in late April.
The BBC said fighting near Bir al-Ghanam began Sunday when government forces tried to cut off the rebels by attacking from the rear.
Since the rebels' weaponry was limited, most of them were focused on a push from the western mountains toward Tripoli, said the rebels' defense leader, Jalal al-Dgheli.
Opposition forces also could soon begin a push toward the capital from the east near Brega.
"What we're learning from defectors is that Gadhafi's supporters are getting fewer, people who are close to him are abandoning him and his inner circle is getting smaller by the day," al-Dgheli told the BBC.
NATO aircraft circled overhead for hours Sunday as rebels in Kikla fought against Gadhafi's forces, the Los Angeles Times reported. In the afternoon, NATO conducted airstrikes in Qawalish, where rebels say Libyan forces store arms.
Libya's official news agency reported the attacks on Qawalish, quoting sources as saying "this aggressive bombardment had caused the martyrdom and injury of a number of people and the destruction of some vehicles."
Three explosions were heard in Tripoli Monday morning, CNN reported.
The Libyan government renewed its offer of conducting an election on whether Gadhafi should stay in power.
The African Union announced during the weekend Gadhafi would not be part of the organization's next attempt to develop a peace deal in Libya, CNN said. It was unclear who would represent the Libyan government in negotiations, or when negotiations would occur.
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