Islamic State (IS) militants in Syria have entered the Unesco World Heritage site of Palmyra after seizing the town next to the ancient ruins, reports say.
Unesco says its destruction would be "an enormous loss to humanity", but no damage has been reported there yet.
IS now controls the nearby airport, prison and intelligence HQ, the Syrian Observatory for Human Rights says.
The militants have previously demolished ancient sites in Iraq that pre-date Islam.
The BBC's Jim Muir in Beirut says acute international concern over Palmyra might actually spur the jihadists on to make destroying the site a priority.
The ancient ruins are situated in a strategically important area on the road between the Syrian capital, Damascus, and the contested eastern city of Deir al-Zour.
Palmyra is also close to oil and gas fields.
Elsewhere in Syria, 40 rebels from Islamist factions were killed in Aleppo when government forces bombed a rebel headquarters, the Syrian Observatory for Human Rights said.
An activist who has family members in Palmyra told the BBC that his relatives wanted to flee but there was no way out.
IS fighters were searching the city for Syrian army soldiers, he said, and residents were being warned via mosque loudspeakers not to hide them.
He also said the inhabitants were angry that Western media are focusing on the ancient ruins, and not the population.
"We still don't have accurate figures about how many civilians there are in Palmyra but there are plenty," he said.
"People think the West cares more about the civilisation than about the people who created or initiated this civilisation."
Tadmur, the Arabic name for the modern settlement next to Palmyra, would normally have a population of around 70,000, but it has recently been swollen by an influx of people displaced from other combat areas.
Syrian state media said pro-government forces had pulled out after "assuring the evacuation" of "most" of its inhabitants.
Talal Barazi, the Governor of Homs Province, which includes Palmyra, told the Associated Press that 1,300 people had fled the city over the past few days, and more were trying to leave.
Rising out of the desert, the site contains the monumental ruins of a great city, which Unesco and others consider one of the most important cultural centres of the ancient world.
Dating back to the 1st and 2nd Century, when the region was under Roman rule, Palmyra is dominated by a grand, colonnaded street.
The Syrian Observatory reported that more than 100 pro-government troops were killed in overnight clashes around Palmyra.
A researcher from the monitoring group also told the BBC on Friday that IS now controls more than half of Syrian territory.
However, the BBC's Arab Affairs Editor Sebastian Usher says this figure may give a false impression because there are large areas to the east under IS control that are not very significant strategically.
Analysis: Jim Muir, BBC News, Beirut
Many questions will now be asked in Damascus and Baghdad - and above all in Washington - about how the militants have managed to score major advances in both Iraq and Syria this week despite all the efforts to stop them.
IS was supposed to be on the defensive in Iraq, where the prime minister announced weeks ago the launching of a campaign to drive the militants out of Anbar province. Now he's lost its capital, Ramadi, just days before they took Palmyra in Syria.
The Western coalition's bombing campaign has clearly hurt IS where it could. But it could never compensate for ground forces which are not competent, equipped or motivated enough to stand firm and hit back.
Only the Kurds in the north of both countries (most recently in north-eastern Syria) have proven able to do that.
Unesco's director-general, Irina Bokova, said any destruction to Palmyra would be "not just a war crime but... an enormous loss to humanity".
"It belongs to the whole of humanity and I think everyone today should be worried about what is happening," she said in a video statement.
Ms Bokova told the BBC that protecting sites like Palmyra had become a security imperative, as well as a cultural concern, because, she claimed, the militias were using trafficked artefacts to get funds:
"These are not some lovers of art," she said.
"This is part of the financing of extremism and it is absolutely imperative that we stop these channels of illicit trafficking."
Syria's head of antiquities, Maamoun Abdul Karim, said on Wednesday that hundreds of Palmyra's statues had been moved to safety but that large monuments could not be transferred.
"This is the entire world's battle," Mr Abdul Karim warned.