"IS thwarted an offensive by Syrian regime loyalists as they pressed an advance some four kilometres (two and a half miles) from Palmyra, and at least 26 fighters were killed," the Syrian Observatory for Human Rights said.
"Warplanes believed to be Russian meanwhile struck parts of Palmyra city and its surroundings in the east of Homs province, as well as Al-Qaryatain in the southeast."
IS seized Palmyra, a UNESCO World Heritage Site known as the "Pearl of the Desert", in May last year, sending shock waves around the world.
In September, satellite images confirmed that the ancient city's famed Temple of Bel had been demolished by IS as part of its campaign to destroy pre-Islamic monuments it considers idolatrous.
Syrian troops and allied militia launched an offensive to retake the city earlier this month.
Observatory director Rami Abdel Rahman said that so far progress had been been "slow", despite some 800 air strikes by Russia and the regime.