Libyan rebels say they have seized the western town of Ghezaia, after launching an offensive in the region on Thursday.
Medical officials say at least two rebels have been killed in fighting with forces loyal to leader Moammar Gadhafi in the area, which is near the Tunisian border.
Mr. Gadhafi's forces have used the town as a base to launch attacks on rebels in the region's mountains.
The fighting comes a day after the head of Libya's opposition council said the council's offer for Mr. Gadhafi to remain in the country if he cedes power has expired.
Mustafa Abdel Jalil said Wednesday that the proposal, which was presented to a United Nations envoy about a month ago, had a deadline attached.
Libyan Prime Minister Al-Baghdadi al-Mahmoudi has said Mr. Gadhafi's departure is not up for discussion.
The Libyan government has also condemned Britain's decision to recognize the opposition Transitional National Council and expel all of Libya's diplomats, calling the moves “illegal and irresponsible.”
British Foreign Secretary William Hague said Wednesday the decision is based on the opposition's increasing legitimacy, competency and success in reaching out to Libyans across the country.
Hague said the opposition council is working toward a more open and democratic Libya, which he said is in “stark contrast” to Mr. Gadhafi, whose “brutality” against the Libyan people has stripped him of legitimacy.