At least 15 fighters under the command of strongman Khalifa Haftar were killed in clashes with forces linked to the UN-recognized government in Tripoli, a security source told the Spanish news agency Efe on Saturday.
If Haftar, who controls eastern Libya, manages to conquer Tripoli, he will gain control of most of Libya.
The clashes were fought on Friday around the town of Kasr ben Ghashir, one of the axes that lead to the former international airport of Tripoli, of important strategic value.
Similar battles were also fought in the neighbouring area of Al Saba, where fighters from the UN-recognised government of Fayez al-Serraj managed to capture three enemy soldiers, the source added.
In response, forces under Haftar's command bombed various positions in the neighbourhoods of Ain Zara and Yarmouk, located in the southern outskirts of the capital, next to the airport.
Since 2011 when Libya's dictator Muammar Gaddafi was overthrown and killed, Libya has descended into factional fighting. If Haftar, who controls eastern Libya, manages to conquer Tripoli he will gain control of most of Libya.
On Friday Euronews spoke to residents of Tripoli who gather each week in the centre of the city and protest against Haftar's offensive.
"We are protesting the act of conquest of Tripoli on behalf of that war criminal called Haftar," one man told Euronews.
"We don’t want death, we don’t want destruction, we want Libyans to live in peace and prosperity," a young woman said.
Another man said: "This is the new generation and the future of the country. They shouldn’t be growing up to take up arms. The army’s time in Libya is finished. We need to start a modern civil state."