Russia, which backs the Syrian government, ordered the daily truce from 9am to 2pm (0700 GMT to 1200 GMT) and the creation of a “humanitarian corridor" to let civilians leave the area, the last major rebel stronghold near Damascus.
Syrian state television broadcast from the government-held area adjacent to Douma, a town in eastern Ghouta where it said the crossing was open. A few people were visible on the road there but it said nobody was leaving the enclave.
State TV reported that militants were trying to shell the corridor to prevent people crossing. But a spokesman for Falaq al-Rahman, one of the main rebel groups, denied anyone was being prevented from leaving.
He told Reuters nobody would dare to approach the area near the corridor because it was a military zone and people feared arrest or conscription if they went over to the government side.
The Syrian Observatory for Human Rights said calm had generally prevailed in eastern Ghouta since midnight, though four rockets had hit Douma in the morning before the ceasefire came into effect.
“Today it is very calm. It is as if they are abiding by the truce they spoke about," said a Ghouta resident in a voice message from the town of Hammourieh. “Nothing happened in our area, and we haven’t heard anything around us."
A witness said ahead of the ceasefire that people in Douma were going out to buy supplies.
“Residents have rushed out of the shelters with their things to go and check on their houses. They are just afraid of being stabbed in the back," said Moayed Hafi, a member of the civil defence rescue service in eastern Ghouta from the town of Saqba.
“There are reconnaissance planes flying high. We don’t know why they are there. May God protect us," he told Reuters.
The Russian defence ministry said on Monday the measures, decided in agreement with Syrian forces, were intended to help civilians leave and to evacuate the sick and wounded.
Russia has accused the rebels of preventing civilians from leaving the area, which the government has besieged since 2013.
The Falaq al-Rahman spokesman, Wael Olwan, said the group had never forced any civilians to leave or stay in the enclave. Writing on Twitter, he accused Russia of presenting people with the choice of forced displacement or being killed in bombardment and siege and called this a “Russian crime".
Eastern Ghouta, where the UN says around 400,000 people live, is a major target for Syrian President Bashar al-Assad, whose forces have clawed back numerous areas with military backing from Russia and Iran.
Even before the latest bombardment began, there was growing international alarm over humanitarian conditions in the region because of shortages of food, medicine and other essentials.
A UN Security Council resolution passed on Saturday had demanded a 30-day truce across Syria.
Fighting has escalated on several fronts in Syria this year, with the collapse of Islamic State giving rise to numerous other conflicts involving Syrian and foreign parties to the multi-sided conflict.
As Assad has pressed the offensive against eastern Ghouta, Turkey has launched an incursion against Kurdish fighters in the northwestern Afrin region.
Tensions have also flared between Iran and Israel, which is deeply alarmed by Tehran’s expanding influence in Syria. Syrian air defences shot down an Israeli F-16 earlier this month as it returned from a bombing raid on Iran-backed positions in Syria.
The Syrian war, which is approaching its eighth year, has killed hundreds of thousands of people and driven half of the country’s pre-war population of 23 million people from their homes.
Russian reports on details of the ceasefire have made no direct mention of letting relief supplies into eastern Ghouta.
The International Committee of the Red Cross in Geneva said on Monday it welcomed any measure that allowed “those who wish to leave to do so, of their free will", as well as medical evacuations.
But spokeswoman Iolanda Jaquemet said much more was required: “The need remains for humanitarian convoys to move in with vital supplies: medicines, medical supplies, food, material to purify the water. This is a place with up to 400,000 people and humanitarian needs are huge." Reuters