The ISIL militants executed 26 civilians, 10 of whom were beheaded, for collaborating with the Syrian government forces, the Syrian Observatory for Human Rights (SOHR) said on its website.
Earlier in the day, SOHR reported that IS militants battled Syrian government forces all across the city of Tadmor, which is about half a mile from Palmyra.
The Syrian government forces were "shocked by the Islamic state making sudden and significant advances" in the area, according to SOHR.
Palmyra contains the monumental ruins of an ancient city that was one of the most important cultural centers of the antique world. Among the surviving buildings are colonnades, temples and a Roman theater.
Vast territories in Syria, which has been in the state of civil war since 2011, are currently controlled by Islamic State. The militants captured parts of Syria in 2012, and in 2014 expanded into Iraq. A number of IS cells are also known to operate in Libya, Yemen and other territories in the Middle East and North Africa.