Mr Assad also promised opposition fighters that those who set free their hostages would escape punishment.
The amnesty offer to rebels who give up their weapons and surrender within three months was issued through a decree on Thursday, the state Sana news agency reported.
It comes amid a recent offensive which has seen government forces tighten a siege on Aleppo.
Mr Assad's offer coincided with a joint announcement by Russia and the Syrian government of a "large-scale humanitarian operation" to "help civilians who were taken hostage by terrorists as well as fighters who wanted to lay down their arms".
Russian Defence Minister Sergei Shoigu said three corridors had been opened for civilians and fleeing fighters, as well as food and first aid points.
It follows warnings from humanitarian groups of a major catastrophe if the siege on the eastern rebel-held parts of Aleppo continued.
Mr Shoigu complained a fourth corridor for militants wishing to surrender had been established in the north of the city because the United States had failed to provide information on the positions of the Free Syrian Army and the al Qaeda-linked Nusra Front.
He said Russia had urged Mr Assad to pardon those who have not committed serious crimes, adding Moscow was sending a top general and experts to Geneva at the request of US Secretary of State John Kerry to discuss the crisis.
State TV said fliers had already been dropped on rebel-held parts of Aleppo, urging people to take up the offer - which includes temporary accommodation.
Earlier this week, the Syrian army said it had cut off Castello Road - the remaining single supply route leading to the rebel-held side of the city.
Aleppo, Syria's largest city before the war, stands divided between rebel-controlled and government-held sectors.