Syrian government forces are trying to drive back Islamic State (IS) from the ancient ruins and famous World Heritage Site of Palmyra in the Syrian desert.
Syrian warplanes and troops are targeting militant positions on the city's eastern edge, activists say.
The UN's top cultural official said the IS advance was "very alarming".
Islamic State has ransacked and demolished several ancient sites in Iraq. Palmrya has already suffered damage during the Syrian civil war.
The Unesco World Heritage site is strategically located on the road between the capital, Damascus, and the contested eastern city of Deir al-Zour. It is also close to gas fields and home to a major airbase.
"Islamic State group jihadists are now 1km (less than a mile) from the archaeological site of Palmyra," the director of the Syrian Observatory for Human Rights, Rami Abdel Rahman, told the AFP news agency.
Using warplanes, he said, "the army is bombing the surroundings of Tadmor from the air", referring to the modern city adjacent to Palmyra.
Syrian state media confirmed the development on Friday, with state-run Sana news agency reporting that troops were "chasing" IS fighters to the north and east of Palmyra.
On its own media outlet, Al-Bayan radio, IS claimed to have attacked a signals tower next to the citadel, setting fire to buildings there, as well targeting the military airport to the east of the town, an oil station and a gas company.
But Syrian officials said on Friday the militants had not yet managed to reach the ancient city, with the governor of Homs telling state media that the site was safe and protected by the Syrian army.
The country's antiquities chief has warned that if IS seizes Palmyra, it will destroy everything there, describing the current fighting as a "battle between civilisation and barbarism".
He has appealed for international intervention to avoid another cultural disaster following the recent destruction of Iraq's ancient sites by IS in Nimrod, Hatra and Mosul.
Outside intervention is highly unlikely despite huge international concern, says the BBC's Jim Muir in Beirut.
With a large military base, vast weapons arsenal and major highway running through it, Palmyra is of high strategic value, which is why the Syrian government forces seem to be fighting so hard to defend it, he adds.
Meanwhile, Unesco chief Irina Bokova said on Friday the heritage site "should not be used for military purposes" and has appealed to both sides to protect it.
Since the IS offensive began on Tuesday, 73 soldiers and 65 militants have been killed, according to AFP. In addition to this, activists say at least 26 civilians were executed - 10 of them beheaded - after they were accused of collaborating President Bashar al-Assad's government.
Rising out of the desert and flanked by an oasis, Palmyra contains the monumental ruins of a great city that was one of the most important cultural centres of the ancient world, according to Unesco.
The site, most of which dates back to the 1st to the 2nd Century when the region was under Roman rule, is dominated by a grand, colonnaded street.