Russian soldiers were charging money to allow people out, up to pounds 10 for a car full of people, one woman said, who had turned back, angry and tearful.
One old couple carrying their belongings in a plastic bag and a red bucket said their house had been destroyed for the third time. "How long will this go on?" the woman asked.
Some refugees waited eight hours on the road as the soldiers checked their documents, calling cars forward one by one with a loud-hailer, while a sniper trained his sights on the approaching vehicle.
"We have been warned that fighters will try to break out this way," said the officer in charge. "We have to check every car; every man who could be a fighter we turn back."
The Russians looked exhausted and demoralised. Fresh bullet marks scarred one wall. "They hit us yesterday," said a soldier called Alexei, a bandanna tied round his head. "One guy was wounded and we are all concussed."
The crash and rumble of heavy artillery sounded constantly as Russian forces began a steady bombardment of the city centre as the heavy rain ceased. Just north of the centre mortars whistled overhead as machine- gun battles erupted around a large Russian command post.
Small groups of Chechen fighters moved among abandoned apartment blocks up to their positions just 200 yards from the compound, where, they said, they had pinned down more than 1,000 Russian troops.
"There are two regiments which have anything from 600 to 1,000 men and a battalion of 200 in there," one said. "We have them completely surrounded; they cannot leave and no one can reach them."
The crack and whistle of a sniper rifle shot rang out. Both sides were sniping at each other from a distance of 200 yards. Occasionally they opened up with a machine-gun or lobbed shells at each other.
A fresh group of a dozen fighters arrived, climbing out of a small Zhiguli car, with rocket-propelled grenades and rifles. They set off on foot to relieve men on the forward positions, running across intersections to dodge sniper fire but otherwise relaxed, even casual. The commander of the unit, who spoke on his walkie-talkie using the code name "Leopard", said they were about to set up a recoilless rifle on the roof of an abandoned five-storey apartment block and fire into the Russian compound.
The fighters' aim in this part of the city seems to be one of containment rather than attack, said one resident, Mago-med, whose brother was among the fighters.
"They shoot at them to keep them pinned down and watch out to stop any reinforcement breaking through."
The Chechens had also isolated three Russian posts, ramshackle strongholds of concrete blocks and sandbags, on the northern road into this district. Between each post on the main road, armed Chechen fighters stood on street corners, milling with residents who started up a small bazaar.
Khesir Dalayev, driving a small truck back towards the centre, said he had brought three wounded fighters out under heavy shellfire the day before. After first aid, they took the wounded on to the neighbouring republic of Ingushetia, he said, just driving around the Russian posts.
"We can do anything we want here," said Mr Dalayev, laughing.