Treason, espionage and terrorism were excluded from the amnesty, SANA said, while possession of illegal weapons and escape were included.
Government-run media said Assad replaced the death sentence with prison terms that include hard labor, the British newspaper The Guardian said on its blog.
The amnesty applies to certain crimes committed before Tuesday.
Among the groups of people eligible in the amnesty were prisoners sentenced to death, people with incurable diseases, the elderly and those who committed misdemeanors, SANA said.
Meanwhile, in a joint appeal for a political solution to the crisis in Syria, leaders of five U.N. agencies Monday called on political leaders to seek a solution quickly, saying their agencies may be forced to suspend some of their support.
Undersecretary-General for Humanitarian Affairs Valerie Amos, Executive Director of the World Food Program Ertharin Cousin, U.N. High Commissioner for Refugees Antonio Guterres, Executive Director of UNICEF Anthony Lake and the World Health Organization Director-General Margaret Chan said in an op-ed published by The New York Times their agencies are working above capacity to aid those affected by the violence, stressing that finding a solution was the only way to stop the growing needs of the population.
"In the name of all those who have so suffered, and the many more whose futures hang in the balance: Enough! Summon and use your influence, now, to save the Syrian people and save the region from disaster," they said.