However, the strikes that began a week ago have hit factions linked with figures opposed to Prime Minister Abdelhamid al-Dbeibah, prompting outrage among critics of the GNU and fears of an escalation.
In eastern Libya, the national parliament that seeks to replace Dbeibah's government, said this week the drone strikes were aimed at "settling political scores", saying one had targeted the home of a parliament member.
Dbeibah has described the drones carrying out the attacks as Libyan although the GNU was not known to possess any. On Thursday he said "those who direct these important and modern planes are Libyans".
Turkey, which sent forces to help the government in Tripoli ward off an assault by eastern forces in 2020, has previously deployed drones from bases in western Libya. Ankara has not commented on the drone strikes.
Zawia, which has one of Libya's main refineries and petrol import terminals, has long been seen as a centre of fuel smuggling and people trafficking. Control over the city has been repeatedly contested over recent years, including by groups that back and oppose Dbeibah.
"The situation in the city is terrible. Armoured vehicles with tinted windows are everywhere. Wedding parades happen with military cars, some carrying medium weapons. Imagine engagement parties with bombs!" said a resident who asked not to be named.
"When you enter the city you can hear gunfire. Clashes break out at any time or place. As ordinary people our life ends before sunset and then it's time for the gangs," said another resident who also requested anonymity.
Any move to restrict fuel movements through the port and refinery by groups in the town could reduce supplies to major power plants, causing electricity cuts in Tripoli.
The United States and other Western countries have voiced concern at the use of weapons in civilian areas of Zawia and urged leaders to calm the situation.
(Reporting by Reuters Libya newsroom; Writing by Angus McDowall; Editing by Frances Kerry)