But there were important exceptions to the types of crime it covers.
The amnesty is applicable to just one crime classified under the Terrorism Act, namely failing to inform the authorities about rebel activity.
Other acts such as possessing leaflets that encourage "terrorism" and taking up arms against the regime are not covered.
"Army deserters may be pardoned, if those still in Syria hand themselves in within 30 days, and those outside Syria hand themselves in within 90 days," said the decree.
"The death penalty will be replaced with a life sentence of hard labour," said SANA, stipulating that "those who financed terrorist groups or who committed terrorist acts that led to death and destruction are not covered".
"Those who conspired to carry out a terrorist act have their sentence reduced by a quarter, and those who knew about such an act and did not inform the authorities are covered by the amnesty," said the decree.
The regime describes Assad's opponents and rebels fighting his troops as "terrorists".
The amnesty will not apply to those who smuggled weapons or drugs, though smugglers of other goods will be covered as long as they pay reparations.
Deserters "who stole weapons from the army's warehouses and refused to obey orders" are not covered by the amnesty, the text added.
Armed civilians who hand their weapons in within 30 days can also benefit, although those who incited sectarian strife or published false news are exempted.
On the eve of Syria's independence day, Justice Minister Najem al-Ahmad said the amnesty "will reinforce social reconciliation, national cohesion, and (cater to) the need to live together on the occasion of this public holiday".
"The amnesty covers the majority of crimes, on different levels," SANA quoted Ahmadi as saying, though it excludes "a small number of crimes, mainly those linked to terrorism, espionage and treason."
State television said the decree would lead to the release of 7,000 detainees.
In Washington, US State Department spokesman Patrick Ventrell shared what he called the "general scepticism" of the opposition to the offer.
"This is something that the regime has said they'd do in the past, but again, there's tens of thousands of political prisoners that remain in Syrian jails," Ventrell told reporters.
And Syrian Observatory for Human Rights director Rami Abdel Rahman told AFP: "It is not the first time Assad passes an amnesty, and this will not lead to the release of tens of thousands of detainees.
"A real amnesty would involve the liberation of all prisoners of conscience and the revolutionaries. An amnesty would mean putting an end to detention."
Assad's latest declaration comes a day before pro-regime television channel Al-Ikhbariya is to broadcast an interview with him.
Deputy Foreign Minister Faisal Muqdad said in an interview with Britain's Guardian newspaper that "there will be no Syria if President Assad steps down.
"If he leaves now before we agree on a political plan among all Syrians, Syria will no longer be on the map."
Assad's regime has been fighting an insurgency that erupted after his forces unleashed a brutal crackdown on peaceful, Arab Spring-inspired democracy protests in March 2011.
The conflict has killed tens of thousands of people and driven more than five million from their homes, including more than one million refugees.
Beirut said Tuesday it will ask for an urgent meeting of the UN Security Council to ask for aid to help it cope with the influx of refugees from Syria, estimated to number 400,000 people.
On the ground, the Observatory said 49 people were killed on Tuesday, adding that the bodies of 31 people shot by snipers were found in the northern city of Aleppo.
In Belgium, police staged early morning raids targeting individuals suspected of sending foreign fighters to fight for radical Islamist groups in Syria.