Syrian government forces have advanced into Palmyra on several fronts backed by air strikes and artillery, a monitoring group says.
The UK-based Syrian Observatory for Human Rights said the fighting was the most intense yet seen in the army's campaign to recapture the city from so-called Islamic State (IS).
IS seized the Unesco World Heritage site and adjoining modern town in May.
It destroyed archaeological sites, drawing global outrage.
Two 2000-year-old temples, an arch and funerary towers were left in ruins.
Government forces had taken neighbourhoods in the western and northern parts of the city, the observatory said.
Syrian state media said earlier the army had taken full control of the al-Amiriya district on Palmyra's northern edge.
TV footage showed repeated explosions and smoke rising from many buildings.
On Friday, Syria's official Sana news agency reported that troops, backed by Russian air strikes, had taken a reconstructed 13th century castle perched on a hill to the west of the Roman-era ruins.
The castle, known as Qalaat Shirkuh or Qalaat Ibn Maan, sits on a 150m-high hilltop overlooking the ruins and is of strategic importance, pro-government media reported.
Government forces briefly entered the town on Thursday but were pushed back.
The prospect of its liberation has been welcomed by Unesco, the UN's cultural agency, which has described the destruction of Palmyra as a war crime.
The jihadist group, which has also demolished several pre-Islamic sites in neighbouring Iraq, believes that such structures are idolatrous.
But the head of Syria's antiquities authority Mamoun Abdelkarim promised to repair as much of the damage as possible as a "message against terrorism".
In addition to its ruins, Palmyra is situated in a strategically important area on the road between the capital, Damascus, and the contested eastern city of Deir al-Zour.
Recapturing Palmyra would be a significant victory for the government and Russia, which withdrew most of its forces last week after a six-month air campaign against opponents of President Bashar al-Assad.
Russia's intervention is widely seen as having turned the tide of the five-year civil war in Mr Assad's favour.
The ancient city of Palmyra