The London-based Syrian Observatory for Human rights said the militants entered Palmyra on December 10 after taking strategic heights near the city and capturing the northern part of Palmyra.
The Syrian Army earlier said it had sent reinforcements to Palmyra, which Syrian troops, backed by Russian air strikes, captured from IS militants in March.
The militants were pushing toward the T4 air base, one of Syria's major military bases, near Palmyra that is used by Russian forces.
The IS offensive on Palmyra, which began on December 8, has left dozens of Syrian soldiers dead.
The observatory said the militants had gained control of some oil and gas fields around the city.
U.S.-led coalition warplanes destroyed 168 oil tanker trucks near Palmyra belonging to IS militants on December 9.