The Syrian advance comes amid a government offensive to capture Palmyra that began earlier this month with support from Russian fighter jets.
A Russian commando who was calling in coordinates for air strikes was killed, said an unidentified Russian military spokesman from the Hmeymim base in Latakia.
“The soldier died heroically, distracting fire onto himself after being discovered by terrorists and surrounded by them,” he was quoted as saying in Russian media on Thursday.
The UK-based Syrian Observatory for Human Rights said fighting was still ongoing outside the city after a rapid advance the day before brought the army and its allies right up to its outskirts.
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.
Syria is in the midst of cessation of hostilities between government forces and opposition rebel factions, which has significantly reduced violence in the country.
The agreement excludes al-Nusra Front and ISIL, which are considered “terrorist” groups by the Syrian government.
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.
Russia’s top commander in Syria, General Alexander Dvornikov, said in an interview published on Wednesday that if Palmyra falls, it could deal a devastating blow to ISIL.
Dvornikov said the ongoing Syrian army offensive will “cut the Islamic State group of forces in two and open the road to Raqqa and Deir ez-Zor, and create conditions for reaching the border with Iraq and establishing control over it”. AL JAZEERA