"The Syrian army is pushing forward from the western parts of the city. Backed by government rocket attacks and air strikes, the army is advancing in its offensive to retake the ancient city of Palmyra," the observatory reported on their website.
Al-Amiriyah town is considered the last line of defence for ISIL, Syria's state news agency, SANA said on Saturday.
"The operations have resulted in establishing full control over the neighborhoods of al-Mutaqaidin, al-Amiriyah and al-Jamiyat al-Gharbiyeh in Tadmur city, according to sources on the ground," SANA reported.
To be restored
SANA said on Saturday that the ancient citadel had been massively damaged by ISIL as it fled into the city.
Palmyra's ancient Roman temples and archway, blown up by ISIL last year, would be restored once the regime recaptured the city, the head of the antiquities authority, Mamoun Abdelkarim told the Reuters news agency on Saturday.
Abdelkarim told Reuters he hoped Palmyra would be retaken within days, after government forces fought their way into the western and northern parts of the city, and promised to revive the Roman-era monuments "as a message against terrorism".
SANA reported on Friday that the army, backed by forces loyal to the government, recaptured the Syriatel hill and the Palmyra castle after heavy clashes with ISIL.
"The army units combed the hill after destroying the last hideouts of ISIS terrorist organisation and dismantled the explosive devices left behind by its members," SANA reported on their website.
SANA also reported that the Syrian army captured al-Qubour valley and al-Qusour Mountains, located 3km west of Palmyra city.
The Syrian advance comes amid a government offensive to capture Palmyra that began earlier this month with support from Russian fighter jets.
ISIL captured the city, also known as Tadmur, in May last year and began a campaign of destroying some ancient sites and using others to stage mass executions.
The uprising that turned into a civil war in Syria began five years ago. More than 250,000 people have since been killed, according to the UN, and millions have fled to neighbouring countries and Europe.
ISIL began capturing large swaths of territory in Syria in 2013 after wrestling territory off rebel groups and later through its own offensives against both the opposition and government.
The group has held on to most its gains but has lost areas in northern Syria to Kurdish groups backed by US air strikes and Syrian forces backed by Russia.