Troops loyal to a rogue general launched air strikes against Islamist militia in Benghazi, a Libyan security official said, in what appeared to be a new push into the city itself as part of his ongoing offensive against the fighters.

The strikes on Sunday followed a ground assault with infantry and clashes earlier in the day that left five dead. Both actions seemed to be part of a plan by General Khalifa Hiftar and his forces to seize control of the eastern city.

The official said Hiftar's forces lost four fighters while a member of an Islamist militia also died in the clashes. Benghazi was deserted late on Sunday, as banks and businesses shut down. The fighting caused power outages in Libya's second-largest city, according to the electricity ministry. Communications networks were also disrupted.

The official said Hiftar's forces were met by fire from Islamist militias in the neighbourhoods of Siddi Faraj and Qawarsha. It appeared to be the first time Hiftar's forces have made a concerted ground assault on parts of the city. They have previously launched attacks from Benghazi's outskirts and carried out limited air strikes.

Sunday's air strikes were carried out using helicopters, the official said. It was not immediately clear what the specific targets were.

Essam al-Jahni, a Benghazi resident, said families fled areas the city centre and its eastern edges, after Hiftar's forces issued a warning to them. He added that Hiftar's forces had deployed tanks to those areas early on Sunday.

Libya has been embroiled in turmoil since the 2011 civil war and the downfall of Muammar Gaddafi. Heavily armed militia born out of the rebel groups that toppled him are now the main power in the country.