UN envoy Staffan de Mistura said reports reaching his office indicated "a significant drop in violence", in a rare respite in Syria's devastating conflict.
De Mistura noted isolated reports of conflict persisted, especially on Monday night, but that by sunrise on Tuesday the broad picture was positive.
The envoy said he had "no information about any UN trucks moving at this stage", demanding "assurances that the drivers and the convoy will be unhindered and untouched".
In second city Aleppo, AFP correspondents in both the rebel-held east and the government-held west reported nearly 24 hours had passed without air strikes or rocket fire.
AFP correspondents in government-held Damascus and its rebel-controlled suburbs reported quiet too, with residents taking advantage of the lull in violence to mark the Eid al-Adha Muslim holiday.
The Britain-based Syrian Observatory for Human Rights reported minor violations by both government and rebel forces in different parts of the country, but no deaths.
However, the truce did not prevent heavy fighting between regime forces and the jihadist Jund al-Aqsa faction in Hama province of central Syria, the monitoring group said.
Damascus accused the opposition of a series of violations, with its ally Moscow saying Syrian government forces were fully respecting the truce but that rebels had violated it 23 times.
"Syrian government troops have completely stopped firing" except in jihadist-held areas, but "the same cannot be said for armed units of the moderate opposition controlled by the US", said Viktor Poznikhir, a senior Russian military officer.
- 'We could sleep' -
US Secretary of State John Kerry had said earlier that it was "far too early to draw conclusions" about the success of the ceasefire but urged all sides to seize the opportunity.
"For all the doubts that remain, and there will be challenges in the days to come, this plan has a chance to work," he said of the deal he agreed on Friday with Russian counterpart Sergei Lavrov.
"I urge all the parties to support it because it may be the last chance that one has to save a united Syria."
The lull in violence was a rare respite for residents of the war-ravaged country, where more than half the population has been displaced and hundreds of thousands live under siege.
"We usually stay up all night with the airplanes, but thank God last night we could all sleep," said activist Hassan Abu Nuh in opposition-held Talbisseh in central Syria.
It was also quiet in the largely rebel-held northwestern province of Idlib, where air strikes killed 13 people only hours before the truce.
In rebel-held eastern Aleppo, children laughed as they ran through the streets, some playing football under a destroyed bridge.
"The truce is good, but it's not enough. We want food to come in," said resident Abu Jamil.
In the government-held west of the city, Habib Badr was enjoying the silence.
"My house is near the Razi hospital and I'm used to hearing ambulance sirens every two or three hours. I haven't heard anything this morning," he said.
The deal is the latest in a succession of attempts to end the fighting in Syria.
It calls for the truce to be renewed every 48 hours, and immediate humanitarian aid access, particularly to civilians living under siege.
By Tuesday afternoon, there were no signs aid had begun moving into those areas, including eastern Aleppo which is surrounded by government troops.
Damascus warned, meanwhile, that all aid going to Aleppo, particularly assistance sent by Turkey, must be coordinated with it and the United Nations.
- Opposition sceptical -
Russia said its troops had been deployed on the key Castello Road running from Turkey into Aleppo that is to become a demilitarised zone under the deal.
If the ceasefire holds for a week, Moscow and Washington will then begin an unprecedented joint campaign to target jihadists, including IS and former Al-Qaeda affiliate Fatah al-Sham Front.
Russia said De Mistura could invite government and opposition representatives to new peace talks "at the very beginning of October".
But there is still deep scepticism about whether the truce will last, with the opposition yet to officially sign on.
A crucial part of the deal calls on non-jihadist rebels to break ranks with Fateh al-Sham ahead of joint US-Russian operations against the group.
But many Islamist rebel groups cooperate closely with Fateh al-Sham, and the biggest of them -- the powerful Ahrar al-Sham group -- has criticised the terms of the Russian-US deal.
Damascus and its allies have backed the truce, but on Monday Assad said his regime remained "determined to recover every area from the terrorists".