The advances have thrown efforts by Haftar's Libyan National Army into jeopardy.
Libya has been split since 2014 between rival factions based in the capital Tripoli and in the east, in a sometimes chaotic war that has drawn in outside powers and a flood of foreign arms and mercenaries.
Haftar, the most powerful commander in the east, has tried since last year to capture Tripoli.
Turkey's backing in the GNA's most recent advance is most visible in the new balance of power in the air, with drones striking LNA forces repeatedly.
The LNA has denied any foreigners are fighting with it, but the United Nations said this month that Russian private military contractor Wagner Group had up to 1,200 people in Libya.