Streams of civilians have been fleeing the Libyan city of Sirte, ousted leader Muammar Gaddafi's birthplace.
Travelling in vehicles packed with belongings, they have been queuing at checkpoints leading out of the city.
Transitional authority forces say they are observing a truce to encourage the remaining civilians to get out, before launching a final assault.
Sirte is one of two major cities still holding out against the National Transitional Council (NTC) forces.
The whereabouts of Col Gaddafi remain unknown.
Hospital under fire
Scores of cars, buses and trucks piled high with household goods lined up at NTC checkpoints on the outskirts of Sirte all Sunday.
The fleeing residents said the situation in the city had deteriorated to such an extent that there was little food and no water or electricity.
"We couldn't leave our homes because of the shelling; we had to leave the city," Ahmed Hussein, travelling with his wife, mother-in-law and two children, told Associated Press news agency.
An International Red Cross team has been into Sirte and says there is an urgent need for medical aid.
The BBC's Jonathan Head, who is in the area, says that with the exodus picking up, anti-government forces hope they can finally take the town.
Reports suggest that Nato forces are continuing to target the area.
One man, Ali, said he and his family were leaving because "we are caught between Nato bombings and shelling by rebels".
"Nato, in particular, is bombing at random and is often hitting civilian buildings," he told the AFP news agency.
NTC fighter Masoud Jema al-Amari, told AFP that Nato had asked them to pull out of the village where Col Gaddafi was born - on the southern outskirts of Sirte - so they could launch air strikes.
Imam Mahmoud Hammoud al-Kaleni, who was leaving the village with his family, said anti-Gaddafi forces had told them they had to urgently leave.
"They came to our house and told us we had one hour to leave. They told us it was safe to leave," he said.
The Geneva-based ICRC says nearly 10,000 people have now left Sirte, with at least a third setting up camp in desert areas just a few kilometres from the city not wishing to travel too far from their homes.
It says that in Sirte itself, people are dying in the main hospital because of a shortage of oxygen and fuel.
An ICRC team was given security clearance from both sides to cross checkpoints and visit the city's Ibn Sima hospital on Saturday.
"The hospital is facing a huge influx of patients, medical supplies are running out and there is a desperate need for oxygen. On top of that, the water reservoir has been damaged," the ICRC said in a statement.
The team was able to pass through the front lines and deliver medical equipment.
However, they could not visit wounded people on the wards as the hospital came under fire.
"Several rockets landed within the hospital buildings while we were there," the leader of the ICRC team, Hichem Khadhraoui, told AFP.
"We saw a lot of indiscriminate fire. I don't know where it was coming from," Mr Khadhraoui said.
Gaddafi loyalists have been putting up stiff resistance in Sirte since NTC troops began their assault several weeks ago.
Bani Walid is the only other remaining centre of resistance against NTC forces.