Residents of Tripoli have spoken of their fear and confusion as clashes between UN-backed government forces and troops loyal to the Benghazi strongman Khalifa Haftar continue in its southern suburbs.

“We are sandwiched between the forces, people are wondering what to do, we are frightened,” said one woman, who asked to remain anonymous, living with her family in the southern suburbs.

“People are saying that going out of the city is safer, we have bags packed, we’re all ready to leave on short notice, but everything we have is in our home. If we leave, vandals may come. They can break in easily, theft is so common here. Then we lose everything. For now we will stay, but I pray it is the right decision.”

The escalation in violence on Monday came as the Tripoli based government announced on Sunday it was launching a counter-offensive against Haftar’s advance that it had named Operation Volcano of Anger.

The woman said teenagers were scouting the streets looking for signs of fighting and to watch out for roving armed gangs. “Its not just militias we have to watch for, there are civilians with weapons on the streets, they are more of a risk than the militias.”

Q&A What is happening in Libya? Show Hide Libya is on the brink of an all-out civil war that threatens to upend years of diplomatic efforts to reconcile two rival armed political factions. An advance led by Khalifa Haftar, the warlord from the east of the country, has diplomats scrambling and the UN appealing in vain for a truce. The French government, the European power closest to Haftar, insists it had no prior warning of his assault, which is closing in on the capital, Tripoli. The outcome could shape not just the politics of Libya, but also the security of the Mediterranean, and the relevance of democracy across the Middle East and north Africa. For more about the fighting in Libya read our quick guide. Photograph: Hani Amara/X03394

With the death toll from days of fighting reaching into several dozens, international organisations continued to evacuate non-essential staff, following the lead of the US which withdrew some of its troops over the weekend.

Both sides exchanged air attacks, with one strike reportedly hitting Tripoli’s Mitiga airport.

The International Organization for Migration said about 2,800 people had been displaced by fighting in a number of outlying suburbs, with fears mounting for about 1,300 migrants detained in two crowded camps at Ain Zara and Qasr Ben Gashir.

One detainee in the Qasr bin Ghashir detention centre told Al Jazeera that they had been without food and water following the outbreak of clashes nearby. “We can see the military,” he told the channel. “The food store is empty [and] the war is still continuing. Even the electricity and water supply stopped.”

The continued advance of the Libyan National Army forces of Haftar, who enjoys foreign backing including from Russia, Saudi Arabia and the UAE, came as the UN called for a truce to allow the wounded and families to escape, with many trapped close to the frontline.

Facebook Twitter Pinterest Khalifa Haftar pictured in Benghazi in 2011. Photograph: Anja Niedringhaus/AP

The violence in the suburbs conflicted with a tense calm in the city centre, where militias loyal to the government of Fayez al-Sarraj patrolled the streets and where shops remained open and residents as followed news of the fighting on televisions in cafes.

But the situation remained confused, not least over which forces controlled key strategic assets. Mitiga airport in the city centre was still open as of Monday afternoon and in the hands of the government, although there were rumours it might close, while there were conflicting claims over who was in charge of the old international airport south of the city.

What does the battle for Tripoli mean for Libya and the region? Read more

On one key contested road south of the city, makeshift barricades of shipping containers filled with sand had also appeared, blocking the road into the capital.

“Most of the fighting still seems to be in the southern suburbs,” said one analyst who had been in contact with staff in Tripoli. “The city centre is quiet.”

“There was even a cultural festival at the weekend that people came out for,” he added referring to an annual trade festival.

In the suburbs of the sprawling, largely low-rise city, it was a different story. “The cowardly bastards are shelling us,” one resident tweeted. “At least three shells landed in the area, one of them very close to where I live and pieces of shrapnel, still hot, found in neighbour’s garden.”

Residents are using smartphones and social media to share information and post warnings about streets under fire, trying to make sense of the ever changing frontlines. “The airport road is shut with heavy fighting ONGOING,” one person tweeted. “Rockets being used so avoid the area.”

One of the most severely affected locations appears to be the frontline town of Gharyan to the south of Tripoli, which Haftar’s forces seized last week, where residents have reported shortages of food and petrol.

The stress of the fighting is compounded by an already crumbling infrastructure. Since civil war broke out in 2014 Tripoli has been divided into a patchwork of militia fiefdoms, these militias fighting periodic street battles every few months. Well before Haftar’s forces launched their offensive, the city was replete with militia checkpoints and earth berms, with kidnappings and shootings common.

“The militias have a habit of stopping cars driven by men, so it is safer to drive with all the family [in the car],” said one resident. “They [militias] will stop and question drivers, they often take cash or phones or even the car if you can’t show its your car.”

The UN-backed government has no security forces of its own, and with much of the public administration in chaos, water, petrol and power shortages have been common for the past four years. Long lines regularly form outside the few banks still operating after a banknote shortage stretching back more than a year.

Haftar’s supporters say the offensive is intended to end Tripoli’s militia chaos and install regular security forces, but residents have the more immediate fear that the street fighting will escalate into a bloodbath.

“Most will not care who wins,” said the woman. “They just want their old life back.”