Syrian soldiers advanced slowly in heavy fighting with Islamic State fighters near Palmyra's ancient ruins on Friday, state media and a monitoring group said, in an offensive which could open up swathes of eastern Syria to government forces.

The recapture of Palmyra, which the Islamist militants seized in May 2015, would mark the biggest single gain for President Bashar al-Assad since Russia intervened in September and turned the tide of the five-year conflict in his favour.

Russian jets have continued to support the Syrian army and its allies as they push their offensive on the desert city, despite Moscow's recent announcement that it was withdrawing the bulk of its military forces.

A Russian special forces officer was killed in combat near Palmyra in the last week, Interfax said, suggesting the Kremlin has been more deeply engaged in the Syrian conflict than it has acknowledged.

Syria's SANA news agency said that the army and an allied militia took more high ground overlooking the city, while the Britain-based Syrian Observatory for Human Rights reported advances by the army amid what it said were heavy clashes.

Observatory director Rami Abdulrahman said the fighting had reached Palmyra's Roman-era ruins, located in the southwest of the city, where he said the army could not rely on air cover because of the risk of further damage to the ancient site.

Islamic State has blown up ancient temples and tombs since capturing Palmyra, something the U.N. cultural agency UNESCO has called a war crime.

The agency welcomed the prospect of Palmyra's recapture, saying it "carries the memory of the Syrian people, and the values of cultural diversity, tolerance and openness that have made this region a cradle of civilization.

"For one year, Palmyra has been a symbol of the cultural cleansing plaguing the Middle East," UNESCO director-general Irina Bokova said in a statement.

Al-Manar, the television station of Lebanon's Hezbollah group, broadcasting live from the outskirts of Palmyra on Friday, showed footage of the ancient city. It was not possible to assess from the long-range shots what damage had been inflicted, but colonnades and several structures appeared to be still standing.