The fierce raids follow the delivery by Russia of new arms including warplanes to its ally Syria.
Raids by warplanes and helicopters using barrel bombs and missiles left at least 12 civilians and 20 extremists dead on Tuesday, the Syrian Observatory for Human Rights said.
Dozens more were wounded in the strikes against targets including a militant headquarters in the city, which the Islamic State group seized along with its UNESCO-listed world heritage site in May.
Since Friday at least 33 civilians and 70 extremists have been killed in an escalating assault by President Bashar al-Assad's aircraft, it said.
Reports of a rapid Russian military build-up in Syria have added to signs of a major shift in a four-year conflict that has killed more than 240,000 people.
According to a civilian doctor at a field hospital in Palmyra, the city is suffering from a lack of staff and medical equipment, Observatory director Rami Abdel Rahman said.
Some of those who died succumbed to their wounds because of a lack of medical facilities, Abdel Rahman said.
Many of the injured were transferred to the province of Raqa, an extremist stronghold exposed to daily strikes.
Most residents fled Palmyra after IS took over the famed city. The extremists have blown up the ancient Temple of Bel and several famed tower tombs.
COMMENTS
Comments are moderated and generally will be posted if they are on-topic and not abusive.
For more information, please see our Comments FAQ