Moamer Kadhafi's hometown of Sirte saw some of the heaviest fighting in a week on Saturday, AFP reporters said, as new regime forces pressed their campaign to capture it from fiercely determined loyalists of Libya's former strongman.
As military casualties mounted, a rocket killed two children when their family joined the desperate exodus of thousands who have already fled a city suffering from a growing humanitarian crisis.
The focus of the latest fighting was the Ouagadougou Conference Centre, a showpiece venue where Kadhafi hosted the launch of the African Union, near where a hospital was brought badly needed supplies by the Red Cross.
A large force of some 100 National Transitional Council (NTC) vehicles, including anti-tank guns and multiple missile launchers, entered the city from the south at around midday (1000 GMT) and circled the compound.
"We are surrounding the Ouagadougou Centre," fighter Osama Blao told AFP as he returned from the front line.
Several NTC fighters said the Red Crescent had asked them to stop firing because Red Cross officials were inspecting the nearby hospital.
Some of the fighters pulled back after two hours of intense clashes, during which loyalist forces used snipers and mortar fire.
In Geneva, a spokesman for the International Committee of the Red Cross said a team had spent about two hours delivering medical supplies and fuel for a generator to the hospital near the Ouagadougou complex before leaving the city.
The spokesman said hospital officials said there were around 200 wounded people inside, and more were expected.
Some of the hundreds of people escaping Sirte said there had been civilian casualties there when residential buildings were hit, either by artillery fire from besieging new regime forces or by NATO air strikes.
"I left with my family as we are caught between NATO bombings and shelling by rebels. NATO, in particular, is bombing at random and is often hitting civilian buildings," said a man who only gave his first name, Ali.
The coast road west to Libya's third-largest city of Misrata was clogged with convoys of fleeing civilians, an AFP correspondent reported.
The two children killed "were torn to pieces," said Ahmed Abu AUD, a field medic on the western side of Sirte. "They collected the body parts in bags."
NTC chief Mustafa Abdel Jalil said that civilians were being given a chance to leave Sirte.
"A chance of two days has been given by the revolutionaries near Sirte so that civilians can leave the city ... It started yesterday (Friday)," he told a news conference in Benghazi.
However, Abdel Jalil gave no indication that this was in any way an ultimatum or that a major assault would follow the end of that period.
Signup to our newsletter and follow us on Facebook and Twitter!
Abdel Jalil claimed the battles for Sirte and the other remaining stronghold of Kadhafi support, the desert town of Bani Walid, were going well.
"The battles for Sirte and Bani Walid are going very well and they are currently fighting on the basis of an organised plan between the two areas," the NTC leader said.
Among those fleeing, Redwan Abdulrahim, whose small truck was piled high with suitcases and other possessions, said the situation in Sirte was increasingly difficult.
"It was really bad. We didn't know where the bullets and rockets were coming from," he said.
Hassan Duha, a commander in the Misrata military council operations room, said a growing number of Kadhafi troops were trying to hide among the escaping civilians.
"They throw away their IDs and they try to come out with the families," he said.
A Kadhafi officer who surrendered on Saturday, Major Mohammed Usba Hanish, told his NTC captors that troops still loyal to the toppled dictator were facing growing shortages.
For days the city has been said to be without electricity, with water scarce, and food and medical supplies dwindling.
At midday (1000 GMT), NTC forces opened an artillery barrage from the east on administrative buildings in the city centre.
"We are targeting buildings where Kadhafi's men are holed up. Our scouting teams have informed us that a lot of mercenaries are still in there and we are striking them too," said Colonel Hussein Idris as he supervised the barrage.
It was not possible to obtain overall casualty figures.
Dr Ahmed Bushrya said from his field hospital that "more than two dozen wounded fighters were brought here, where there were three martyrs so far in fighting today."
At a field hospital west of Sirte, medics said they had 11 wounded on Saturday.
Dozens of Pakistani migrant workers were among the hundreds of Sirte residents fleeing to the east.
"NATO struck one big building, Imarat Tamim, two days ago, with 12 or 13 bombs," said Ashiq Hussein, who fled the city with 11 family members, including six children.
"The whole building with nearly 600 flats is razed to the ground now."
In other developments, the NTC said that almost 7,000 SAM-7 anti-aircraft missiles from Kadhafi's arsenal had gone missing, while a man claiming to be Kadhafi's spokesman Mussa Ibrahim denied claims he had been captured by NTC forces.
And an official with Tripoli's Mitiga airport said a Turkish Airlines passenger plane had landed there, the first commercial flight to the capital since Kadhafi's ouster.