The decree, published by state media, said the amnesty did not include "criminals" and those on the run unless they turn themselves in to authorities. Deserters in Syria have four months to do so; those abroad have six months.
Since Syria's conflict began in March 2011, tens of thousands of soldiers have either deserted their posts or defected and joined rebels trying to remove Assad from power. The amnesty also includes draft dodgers.
The new amnesty does not include army defectors, some of whom are still fighting against the government, mostly in the northwestern province of Idlib, the last major rebel stronghold in the country. The amnesty could encourage the return of refugees, some of whom have not been able to go back home because they were blacklisted for running away from military service. Other men have feared that if they return they will be punished or forced to join the military.
More than 5 million Syrians have fled their country since the conflict began, while millions of others have been internally displaced. The seven-year war has also killed more than 400,000 people and left more than a million wounded.
The decree comes at a time when government forces have managed over the past year to capture wide areas once held by insurgents, including in southern Syria and the eastern suburbs of the capital, Damascus. In some areas, the government reached reconciliation deals with rebels who were given amnesty in return for laying down their arms.
The flashpoint in Syria is now in Idlib, where insurgents have been withdrawing their heavy weapons from a demilitarized zone agreed upon by Turkey and Russia last month. The deal sought to avoid a wide government offensive on the province.
On Monday, Turkey's official news agency reported that Syrian rebels finished withdrawing all their heavy weapons from the front lines in implementation of the deal reached last month that's expected to demilitarize a stretch of 15-20 kilometers (9-12 miles) along the front lines by Oct. 15.
The Britain-based Syrian Observatory for Human Rights, a war monitor, said all the area along the front lines in Idlib are now free of heavy weapons after rebels and other militant groups, including al-Qaida-linked fighters, have removed or hidden their heavy arms.
Associated Press writer Albert Aji contributed to this report from Damascus, Syria.