The temporary truce, brokered by Washington and Moscow, is seen as a crucial step towards ending a conflict that has claimed 270,000 lives and displaced more than half the population.
It survived a shaky first day, during which state media said shells were fired on the capital while rebels also accused government forces of "violations".
"I think this is the first time we've woken up without the sound of shelling," said Ammar al-Rai, a 22-year-old medical student in Damascus.
"The United Nations, the United States and Russia have made a positive assessment of the first hours of the cessation of hostilities," a Western diplomat said after a meeting of the International Syria Support Group in Geneva.
The UN reported "some incidents" in apparent violation of the truce, but "they have been defused", he said.
Russian Foreign Minister Sergei Lavrov's office said he and US Secretary of State John Kerry had "hailed" the ceasefire in a phone call, and discussed ways of improving cooperation between their militaries.
A spokesman for the UN's humanitarian affairs office said the next convoys are expected to leave today, after aid reached tens of thousands of people in besieged cities over the past week.
"If it (the truce) holds, it will create the conditions for full, sustained and unimpeded humanitarian access throughout Syria," said EU foreign policy chief Federica Mogherini.
The ceasefire faces formidable challenges, however, particularly as it excludes the powerful Islamic State (IS) jihadist group and Al-Qaeda's Syria affiliate Al-Nusra Front.
Moscow has vowed to keep striking IS, Al-Nusra and other "terrorist groups", but said it grounded its warplanes in the Syria campaign on the first day of the truce to avoid potential "mistakes".
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