The contaminant has been linked to the deaths of more than 300 children in Africa and Asia
"Despite heavy losses in manpower and equipment, the terrorists are trying as hard as possible to secure a foothold inside the city," Interfax quoted a statement from the center as saying on Sunday.
"Syrian troops are fighting to defend Palmyra," it added.
The center said Islamic State was drawing on "significant forces" from its strongholds in Raqqa and Deir al Zor.
Earlier on Sunday, a news agency affiliated with the militants and a Britain-based monitoring group said Islamic State recaptured Palmyra after briefly retreating in the face of heavy Russian air strikes.