ISIL fighters have withdrawn from much of the Syrian oasis city of Palmyra as government forces slowly enter its ravaged ancient ruins because of landmines and suicide bombers, a war monitor said on Thursday.

Russian-backed Syrian troops pushed into a western neighbourhood of the city late on Wednesday after fierce clashes with the ISIL fighters.

By Thursday morning, Islamic State of Iraq and the Levant cadres had withdrawn to residential neighbourhoods in the east of the city, the UK-based Syrian Observatory for Human Rights said.

"IS withdrew from most of Palmyra after laying mines across the city. There are still suicide bombers left in the eastern neighbourhoods," Syrian Observatory head Rami Abdel Rahman told AFP news agency.

"Government forces have not yet been able to enter the heart of the city or the eastern parts."

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Palmyra's ancient ruins have long been listed by UNESCO as a world heritage site.

Before ISIL entered the city in May 2015, the city boasted temples, colonnaded alleys, and elaborately decorated tombs that were among the best preserved classical monuments in the Middle East.

But the armed group launched a campaign of destruction, the scale of which was fully revealed when government forces briefly retook the city with Russian support last year.

Satellite imagery has shown that ISIL has demolished more monuments since it recaptured Palmyra from government forces in December.

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Supported by Russian air strikes and ground troops, Syrian government forces have battled through the desert for weeks to reach Palmyra.

The Syrian conflict started as a largely unarmed uprising against President Bashar al-Assad's rule in March 2011.

It quickly morphed into a full-scale war that has killed hundreds of thousands of people with more than half of the country's population displaced inside and outside of Syria.