Lakhdar Brahimi, who represents the UN and the Arab League, is in Damascus to press both the government and the rebels to observe a truce over the Muslim festival of Eid al-Adha.
On Friday, Lakhdar Brahimi met with Foreign Minister Walid Muallem and opposition leaders.
There has been no sign of the violence abating, with an explosion reported in a Christian area of Damascus on Sunday.
The attack apparently targeted a police station in the Bab Touma district of the old city.
Unconfirmed reports say at least one person was killed and several injured.
Heavy clashes were also reported on the main road between Damascus and Aleppo on Saturday, particularly around the town of Maarat al-Numan.
The town has been in rebel hands for more than a week and is seen as strategically important to maintaining a supply route between Syria’s largest city Aleppo and the capital Damascus.
Civilians in Syria are desperate for a ceasefire but many doubt President Bashar al-Assad’s forces will agree.
A ceasefire that started on 12 April was soon broken and more violence prevailed.
Lakhdar Brahimi is calling for a ceasefire over the festival of Eid al-Adha, which begins on Friday and lasts over the weekend.
For much of the past 18 months, rebel groups have been fighting against Bashar al-Assad’s government and at least 30,000 people are believed to have been killed.
Repeated efforts by the international community to find a diplomatic solution have foundered because of a deep divide at the UN Security Council.
In videos posted online, one rebel group said it was willing to respect a ceasefire given certain conditions, while other groups have not made a decision.
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