The most fierce clashes take place on the outskirts of the airfield which is located about 50 kilometers (31 miles) from the city.
Sources told Syrian al-Watan newspaper that the first wave of attacks from terrorists of Daesh was successfully repelled and their attempts to take control of the road from Ferkales region to the airfield have failed.
"The Syrian Army with the support of militia units has regained control of the air defense artillery battalion located near the city," the unnamed source told the newspaper. He added that Daesh is suffering heavy losses both of personnel and equipment.
Another source claimed that Daesh terrorists don't let civilians leave Palmyra under threat of death, Sputnik reported.
On Sunday, Daesh recaptured the ancient city of Palmyra in the Homs province. According to various sources, the number of terrorists that took part in the storming of the city reached 5,000 including hundreds of suicide bombers and dozens of armored vehicles. According to the Homs governor, the government forces managed to evacuate some 80 percent of city's civilian population.