The Syrian Observatory for Human Rights, a UK-based group that reports on the war, also said Islamic State militants had executed 23 people on Friday including nine minors and five women in areas seized from state control outside the city.
Syrian government antiquities chief Maamoun Abdulkarim said fighting continued at 1-2 km (around a mile) from the city, which he said was still “firmly under government control”. A military source said fighting was ongoing but at “a distance far from the city”.
Abdulkarim, speaking by telephone, added: “We are in the fourth or fifth day (of the attack). What is the international community doing? Is it waiting to weep and despair as it did in northern Iraq?”
Palmyra, also known as Tadmur, is home to extensive ruins of one of the most important cultural centers of the ancient world. It was put on UNESCO’s list of World Heritage in danger in 2013.
Islamic State, which espouses a puritanical Islamist ideology, has destroyed antiquities and ancient monuments in Iraq. Palmyra is also of strategic importance, sitting at a highway intersection linking it to the cities of Homs and Damascus, some 240 km (150 miles) to the southwest.
UNESCO has expressed deep concern over reports of fighting near Palmyra.
The Syrian government is a pariah to states in the West and in the region that say President Bashar al-Assad has lost legitimacy, complicating any international effort to protect the country’s cultural heritage.
A military source said the army had reinforced the city.
But the army is under pressure, having lost ground to other insurgents in the northwest and in the south since late March.
The Observatory reported that Islamic State had seized a gas field to the east of Palmyra – a report denied by the military source. The source said Islamic State was keeping up its attack but the fighting on Saturday was at a lower intensity.
The mass execution reported by the Observatory is the second such killing it has recorded since Islamic State advanced this week into the area. In the first, the Observatory said the jihadists had executed 26 men, beheading 10 of them.
The Syrian military source said there had been one massacre of 30 or more people in that area, including elderly men.
The Syrian military has been mounting air strikes against Islamic State fighters in the area. Rami Abdulrahman, who runs the Observatory, said the sides were fighting near a military intelligence building in Palmyra on Saturday.
The Islamic State offensive in central Syria has added to the pressures facing government forces that have faced significant setbacks since late March in the four-year-long war.
Other insurgent groups fighting President Bashar al-Assad have seized control of wide areas of the northwestern province of Idlib since late March. Assad has also lost a border crossing with Jordan in the south.
This week the Syrian army and the allied Lebanese group Hezbollah have driven insurgents from wide areas of the mountainous region to the north of Damascus, shoring up Assad’s grip over the border zone between Syria and Lebanon.