"Assad said that he would not mind taking part in the presidential elections if the Syrian people considered [it] necessary," Sputnik News cited Russian Communist Party member Alexander Yushchenko as telling RIA Novosti on Sunday.
"The meeting with Bashar Assad just ended," Yushchenko said.
"We have discussed…the effectiveness of the operation by the Russian Aerospace Forces," Communist Party member Sergei Gavrilov added.
On September 30, Russia began launching pinpoint airstrikes at Islamic State in Iraq and the Levant (ISIL) positions in Syria at Assad's request.
"He [Assad] proposed a possibility of holding parliamentary elections with all political powers that want peace and stability in Syria," Gavrilov told RIA Novosti.
"We have agreed to meet with him [Assad] in Moscow, with the head of the Syrian parliament, with the Grand Mufti of Syria," the lawmaker added.