Defence ministry spokesman Lt Gen Sergei Rudskoi said the Syrian army was poised to defeat IS militants there.
But US officials said Russia staged no air strikes in Syria in the past week.
The strikes come days after President Vladimir Putin ordered the withdrawal of most Russian forces from Syria.
IS militants captured the ancient city of Palmyra last May.
Since then it has blown up monumental temples, arches and statues in the Unesco World Heritage site, bringing global condemnation.
Meanwhile, IS claimed on Friday it had killed five Russian soldiers in fighting around Palmyra in recent days.
Russia has not commented on the claim and there is no independent verification.
In recent months, IS has been losing ground to President Bashar al-Assad's forces, rebel groups, and Kurdish militia fighters.
Gen Rudskoi told reporters in Moscow that the Syrian army had also seized key hilltop areas near the city of Aleppo and cut supply routes leading to the IS-held city.
US Central Command spokesman Patrick Ryder said there had been some bombardments in the Palmyra region but that they were thought to be made by Russian artillery.
Russia had withdrawn most if not all of its strike aircraft and there had been little movement of its ground forces, Col Ryder said.
Indirect peace talks aimed at resolving the Syrian conflict have been taking place in Geneva for the past week, but so far shown no progress.
Russia says its warplanes are carrying out up to 25 air strikes a day around the Syrian city of Palmyra in support of Syrian forces trying to oust so-called Islamic State (IS).