"Yesterday evening, we moved the tanks ahead. We also shelled the neighbourhoods in the evening for some time," said Mubarak Sharif, radio operator for a senior commander.
"But since then it has been very sporadic."
An AFP correspondent heard only intermittent rocket and small arms fire around the Dollar and Number Two residential neighbourhoods in the northwest of the city where Gaddafi loyalists are holed up.
Another National Transitional Council fighter told AFP that there had been an exodus of civilians from the two neighbourhoods in early morning and that the besieging troops were eager to give others the chance to leave.
"Around 30 families fled the neighbourhoods around 6 am (0400 GMT) and, looking at them, we are holding fire so that others can also flee," fighter Ahmed Farjani told AFP.
The lull contrasted sharply with Saturday afternoon when Kadhafi loyalists mounted a fierce counter-attack, forcing back the NTC fighters under a barrage of rockets and shelling. A medic at a field hospital behind the eastern front line said four NTC fighters were killed and 22 wounded in the fighting on that side of the city of Saturday.
"Those killed were mainly from sniper bullets. And the wounded were injured by explosions and rocket attacks," Dr Ahmed Bushariya told AFP. A commander on the western side of the city echoed the concern about the sniper threat.
"At the very front line, they have very professional snipers," said Salah al-Jabo. "According to doctors, 80 per cent of the fighters killed in the last two days were shot in the head or in the chest."
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