"Russian helicopters and warplanes, that are likely Russian, are bombarding Islamic State group positions near Palmyra," said Syrian Observatory for Human Rights director Rami Abdel Rahman.
"These strikes have allowed regime troops to advance, and they are now four kilometres (2.5 miles) south and west of Palmyra," he told AFP.
The strikes came a day after Russian President Vladimir Putin ordered the pullout of the "main part" of his forces from the war-torn country.
A security source in Syria confirmed the monitor's report.
Also Read
Should the regime retake Palmyra, "it would be an important victory because it would open the way towards the Iraqi border", he added.
IS seized Palmyra, a UNESCO World Heritage Site in eastern Syria known as the "Pearl of the Desert", last May, sending shockwaves across the world.
In September, satellite images confirmed that the Temple of Bel, the main one at Palmyra, had been targeted by IS as part of a campaign to destroy pre-Islamic monuments, tombs and statues it considers idolatrous.