The troops, under the command of Colonel Suhei al Hasan, also occupied hills near the city of Qrayaten.
In a statement the Syrian military said that well-equipped military detachments with a high level of combative training had organized assaults at two locations where ISIL groups are entrenched.
The Syrian army offensive aims to cut all supply lines to terrorist cells and isolate them in this desert region.
Besides the strategic and historical importance of Palmira for the Syrian nation, freeing it is a step towards liberating Deir ez-Zor, which has been besieged by the ISIL since May 2015.
These regions have oil and gas deposits as well as a network of gas pipelines.
sgl/Ym/abo/lma/pgh
PL-30/MNA