Reports say hundreds of people have been killed in a week of bombardment of the Eastern Ghouta enclave near the capital.
The Security Council unanimously called for a 30-day truce “without delay”, but some areas are not covered.
Today Iran, an ally of the Syrian government, said it would target Damascus suburbs held by “terrorists”.
The UN resolution was agreed to allow for aid deliveries and medical evacuations, but operations against the biggest jihadist rebel groups are not covered by the truce.
Activist groups in Syria said government air strikes took place in the rebel enclave soon after the resolution was agreed in New York.
At least three people are reported to have died in the latest attacks, while one rebel group in the Eastern Ghouta said it had killed a number of government soldiers.
The strikes targeted the outskirts of Douma, the main town in the Eastern Ghouta, the UK-based Syrian Observatory for Human Rights (SOHR) said.
The SOHR also reported several casualties on both sides after Syrian government forces clashed with rebels in southern areas of the enclave.
Syrian forces launched a ground offensive to enter the Eastern Ghouta, both opposition and pro-government sources said on Sunday (today).
Meanwhile, Iran said that while it would “adhere” to the ceasefire, it would continue its military operations in areas around Damascus that were not covered.
Iran, along with Russia, is a key supporter of Syrian President Bashar al-Assad and has played a vital role in enabling him to recapture territory across the country.