Soldiers traded rocket fire with Gaddafi loyalists as they edged from the eastern suburbs into the city.
The advance comes two days after the soldiers, loyal to the National Transitional Council (NTC), attacked from the west before retreating again.
Sirte is one of the last remaining strongholds of Gaddafi loyalists. Civilians have been streaming out of the city - some of them were not aware that Tripoli had fallen.
Many of them were terrified, having been told that rebel fighters would slit their throats if they ventured out of the city. The remaining civilians are in increasing danger, caught in the middle of intensifying fighting.
Gaddafi loyalists have been fiercely protecting the city from NTC advances in recent weeks. The NTC troops were forced to retreat on Saturday after getting very close to the centre from the west.
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