The Syrian army, announced the truce at 7 pm (1600 GMT), the moment it took effect, saying the seven-day "regime of calm" would be applied across Syria. It reserved the right to respond with all forms of firepower to any violation by "armed groups".
Rebel groups fighting to topple President Bashar al-Assad did not immediately declare publicly whether they would respect the ceasefire, but rebel sources said they would do so, despite reservations about a deal they see as skewed in Assad's favor.
A rebel commander in northern Syria said there was "cautious calm" at the start of the ceasefire.
The Syrian Observatory for Human Rights, a Britain-based monitoring group, said calm prevailed on most frontlines after the ceasefire took effect.
Russia is a major backer of Assad, while the United States supports some of the rebel groups fighting to topple him.
The agreement's initial aims include allowing humanitarian access and joint U.S.-Russian targeting of jihadist groups, which are not covered by the agreement.
The agreement comes at a time when Assad's position on the battlefield is stronger than it has been since the earliest months of the war, thanks to Russian and Iranian military support. Hundreds of thousands of Syrians have been killed in the conflict and 11 million made homeless in the world's worst refugee crisis.
Hours before the truce took effect, an emboldened Assad vowed to take back all of Syria. In a gesture loaded with symbolism, state television showed him visiting Daraya, a Damascus suburb long held by rebels but recaptured last month after fighters surrendered in the face of a crushing siege.
"The Syrian state is determined to recover every area from the terrorists," Assad said in an interview broadcast by state media, flanked by his delegation at an otherwise deserted road junction. Earlier he performed Muslim holiday prayers alongside other officials in a bare hall in a Daraya mosque.
He made no mention of the ceasefire agreement, but said the army would continue its work "without hesitation, regardless of any internal or external circumstances".
The ceasefire is the boldest expression yet of hope by the administration of U.S. President Barack Obama that it can work with Russian President Vladimir Putin to end the war. All previous diplomatic initiatives have collapsed in failure.
The Obama administration opposes Assad but wants to shift the focus of fighting from the multi-sided civil war between Assad and his many foes to a campaign against Islamic State, an ultra-hardline jihadist group that controls swathes of Syria and neighboring Iraq.
The ceasefire deal is backed by foreign countries ranging from Assad's ally Iran to Turkey, one of the main supporters of groups fighting to overthrow him.
But maintaining the ceasefire means overcoming big challenges, including separating nationalist rebels who would be protected under it from jihadist fighters who are excluded.
The rebels say the deal benefits Assad, who took advantage of the aftermath of the last failed truce hammered out by Washington and Moscow in February to improve his forces' position on the battlefield.
The capture of Daraya, a few kilometers from Damascus, has helped the government secure important areas to the southwest of the capital near an air base. The army has also completely encircled the rebel-held half of Aleppo, Syria's largest city before the war, which has been divided into government and opposition-held zones for years.
BOMBING BEFORE TRUCE TAKE EFFECT
In the hours before the ceasefire took effect, fighting raged on several key frontlines, including Aleppo and the southern province of Quneitra.
The commander of a Free Syrian Army (FSA) group in northern Syria said government warplanes had been bombing "like crazy" on Monday, hitting one of his bases.
"They are using their planes to hit everywhere - Aleppo, Idlib, the rural areas," Hassan Haj Ali, commander of the Suqour al-Jabal group, told Reuters.
Under the agreement, Russian-backed government forces and opposition groups are expected to halt fighting for a while as a confidence building measure. Opposition fighters are expected to separate from militant groups in areas such as Aleppo.
But distinguishing protected rebels from jihadists is difficult, particularly with regards to a group formerly called the Nusra Front, which was al Qaeda's Syria branch until it changed its name in July.
The group, which now calls itself Jabhet Fateh al-Sham, has been playing a vital role in the battle for Aleppo allied with other rebel factions. It remains excluded from the ceasefire, and other rebel groups say government forces or their allies can use its presence as an excuse to hit other targets.
Washington has said the ceasefire includes agreement that the government will not fly combat missions in an agreed area on the pretext of hunting fighters from the former Nusra Front. However, the opposition says a loophole would allow the government to continue air strikes for up to nine days.
Nationalist rebel groups, including factions backed by Assad's foreign enemies, wrote to Washington on Sunday to express deep concerns. The letter, seen by Reuters, said the opposition groups would "cooperate positively" with a ceasefire but believed the terms favored Assad.
It said the ceasefire shared the flaw that doomed the previous truce: a lack of guarantees or monitoring mechanisms. It also said Jabhet Fateh al-Sham should be included, as the group had not carried out attacks outside Syria despite its previous ties to al Qaeda. Jabhet Fatah al-Sham said the deal aimed to weaken the "effective" anti-Assad forces, and to "bury" the revolution.
A source in the opposition told Reuters the powerful Islamist group Ahrar al-Sham, which fights in close coordination with Jabhet Fatah al-Sham, would back the cessation of hostilities in an announcement later on Monday.