If the truce holds for one week, the United States and Russia will work together to carry out strikes against DAESH and Jabhat Fateh al-Sham targets in Syria.
A nationwide ceasefire came into effect in Syria on Monday with the main opposition groups yet to officially announce whether they would agree to a deal brokered by Russia and the United States.
The ceasefire deal, which came into force at 7:00 pm local time (16:00 GMT), is initially aimed at halting the fighting between the Syrian regime and opposition groups and includes improved humanitarian aid access and joint US and Russian targeting of DAESH.
But it faces big challenges, including how to separate Syria's main armed opposition groups from those excluded from the truce.
"Today from 1900 (local time) the cessation of hostilities is being resumed across all the territory of Syria," senior Russian military official Sergei Rudskoi said at a briefing, adding Russia would "continue to carry out strikes against terrorist targets."
The initial 48-hour ceasefire can be renewed for another 48 hours at a time, the Russian Foreign Ministry said in a statement, while adding that Moscow was counting on Washington to influence Syria's "moderate opposition" to ensure full compliance with the cessation of hostilities
If the truce holds for one week, the United States and Russia will then work together to carry out strikes against DAESH and Jabhat Fateh al-Sham, which was formerly known as al-Nusra Front.
In a press conference after the ceasefire came into effect, US Secretary of State John Kerry said the deal could be the 'last chance to save Syria'.
"For all the doubts that remain -– and there will be challenges in the days to come -– this plan has a chance to work," Kerry told reporters in Washington.
"We believe that the only realistic and possible solution to the conflict is ultimately a political outcome," he said, calling for a return to UN-mediated peace talks.
"And I urge all the parties to support it because it may be the last chance that one has to save a united Syria."
The Syrian regime forces announced it would halt 'operations' for a period of seven days as the truce went into effect.
But in a sign that the deal could be extremely fragile, Assad said his forces would continue their work "without hesitation, regardless of any internal or external circumstances".
"The Syrian state is determined to recover every area from the terrorists," Assad said in an interview broadcast by state media hours before the ceasefire went into effect.
Syria's major opposition groups will issue a statement in the coming hours but indicated that they may back the truce under 'harsh reservations'.
"The decision is taken," a source in the opposition, speaking on condition of anonymity, was quoted as saying by Reuters.
"In the next few hours there will be a statement where we state that, but there will be a lot of harsh reservations and observations regarding the whole package. But as a final takeaway, we do agree."
The source said the acceptance had already been communicated to the United States.
The opposition groups say the deal benefits Assad, who appears stronger than at any point since the early days of the war, with military support from Russia and Iran.
The capture of Daraya, a few kilometres (miles) from Damascus, followed years of siege and bombardment and has helped the regime secure important areas to the southwest of the capital near an air base.
Backed by Russian air power, Assad's forces have also completely encircled the opposition-held half of Aleppo. Syria's largest city before the war, Aleppo has been divided into regime and opposition-held zones for years.
'Most of Syria calm'
The Russia-US deal is the second attempt to bring about a ceasefire this year, after an agreement concluded in February collapsed as each side blamed the other for violations.
Washington, which supports some opposition factions, has been seeking to refocus the fighting in Syria on DAESH, which still controls swathes of the country and has not been included in any ceasefires.
The Syrian Observatory for Human Rights said major conflict zones in Syria were calm after a ceasefire took effect but there was some shelling by both the regime forces and the opposition.
"Calm is prevailing," Observatory Director Rami Abdulrahman told Reuters, giving an early assessment of the impact of the agreement brokered by the United States and Russia.
The Syrian war has killed hundreds of thousands of people and forced 11 million people from their homes in the world's worst refugee crisis.