Field Marshal Khalifa Haftar's Libyan National Army said they carried out air strikes on Wednesday on a coastal road west of Sirte, a day after nine of their men were killed in a strike by rivals.
They took control of Sirte, a strategically important city in the centre of Libya's Mediterranean coastline, in a rapid advance on Monday and is seeking to consolidate the gain.
Since April, the LNA has also been waging a campaign to take the capital, Tripoli, about 370km northwest of Sirte, where it is battling forces aligned with the internationally recognised Government of National Accord.
GNA forces said they withdrew from Sirte to avoid bloodshed.
Those forces are mainly from the port of Misrata, 190km east of Tripoli, and had controlled Sirte since driving Islamic State from the city in late 2016.
On Tuesday afternoon, clashes broke out around Al Washka, on the road between Sirte and Misrata, where LNA sources said nine of their men were killed in an evening drone strike.
On Wednesday, the LNA responded with strikes near the Abu Grein checkpoint, close to Al Washka, where clashes were continuing, LNA military officials said.
Libya has been divided since 2014 into rival camps based in Tripoli and the east, each with its own set of institutions.
Turmoil in Libya, where strongman Muammar Qaddafi's long rule was toppled in 2011, has in recent years disrupted the Opec member's oil production, fuelled migrant smuggling to Europe, and given space to Islamist extremists.
Regional powers have upped intervention.
The European Union's top diplomat and the foreign ministers of Britain, France, Germany and Italy this week condemned Turkey's plans to send military experts and trainers to Libya, saying interference was exacerbating instability