"Sunday was the calmest day since the ceasefire came into effect" on February 27, Rami Abdel Rahman, head of the Britain-based Syrian Observatory for Human Rights, told AFP.
He said the exceptions were dozens of rockets fired by Al-Nusra Front, a jihadist group excluded from the truce, and other rebel factions at Kurdish forces in the far north of the city of Aleppo.
The violence killed three people, according to both the Observatory and the Kurds.
Abdel Rahman said the average number of civilian deaths a day has fallen by 90 percent since the ceasefire came into force nine days ago, with an 80 percent decline among soldiers and rebel forces.
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In Moscow, the defence ministry reported 15 ceasefire violations during the previous 24 hours, compared with nine on yesterday and 27 the day before.
Four people were wounded in shelling by unidentified forces of residential areas and loyalist positions in the Damascus area, it said.
Russia's foreign ministry said US Secretary of State John Kerry and his Russian counterpart Sergei Lavrov in a telephone call today welcomed "the sharp decline in violence" and warned against "any delay in starting the process" of negotiations.
Since the failure of a first round of peace talks in 2014, the main sticking point in the negotiations has been the fate of Syria's President Bashar al-Assad.
He has refused to step down since peaceful protests in early 2011 developed into a multi-faceted war that has killed more than 270,000 people and displaced millions more.