Islamic State fighters reached online said the group was shelling an air base near Tadmur, an oasis in the desert north-east of Damascus also known as Palmyra.
The Syrian Observatory for Human Rights monitoring group said the militants had taken up positions outside the town, which is listed as a UNESCO World Heritage site, after capturing al-Sukhna, 75 km (46 miles) to the northeast, on Wednesday.
An army source said fighting continued in al-Sukhna for a second day on Thursday and troops were still in their positions.
The Syrian military and allied Lebanese militants have been pushed back in the northwest and south recently, but this week cleared insurgents from mountains near the Syria-Lebanon border north of Damascus in a notable advance.
The Observatory reported heavy casualties on both sides in fighting near al-Sukhna on Wednesday, with at least 70 troops and 40 Islamic State fighters killed.
It would be the first town taken by Islamic State in direct fighting with government forces. Others seized by the group in the north and east were taken from other insurgents.
Islamic State has in recent months mounted frequent attacks on government- and rebel-held areas to the west of its strongholds in Deir al-Zor and Raqqa provinces, where its fighters have been facing air strikes by a U.S.-led coalition.
Tadmur, which has previously been a frontline in the four-year-long Syrian conflict, was included in UNESCO’s list of World Heritage in danger in 2013, according to the UNESCO web site. It contains the monumental ruins of a city that was one of the most important cultural centers of the ancient world.
The ultra-radical Islamist group has systematically destroyed antiquities in Iraqi territory it seized last year.
The military source said Syrian forces had inflicted heavy losses on what it said were many Islamic State fighters targeting al-Sukhna. “They are attacking in large numbers like cattle with heads facing the ground,” the source said.
The army had yet to confirm losses in its ranks, the source added.
Syrian state media said Islamic State fighters were being hit by Syrian army air strikes, adding that an Islamic State convoy had been destroyed to the east of al-Sukhna.
Since March, the Syrian army and allied militia have lost control of wide areas of the northwestern province of Idlib, and also a crossing at the border with Jordan.