A roadside bomb detonated as a bus passed and a suicide bomber blew himself up in the Bab al-Saghir area, which houses several Shiite mausoleums that draw pilgrims from around the world, the Syrian Observatory for Human Rights said.
Several Shiite pilgrims were among the dead.
“There are also dozens of people wounded, some of them in a serious condition,” Observatory chief Rami Abdel Rahman told AFP.
Shiite shrines are a frequent target of attack for Sunni extremists of Al-Qaeda and the Islamic State group (IS), not only in Syria but also in neighbouring Iraq.
The Sayeda Zeinab mausoleum to the south of Damascus, Syria’s most visited Shiite pilgrimage site, has been hit by several deadly bombings during the six-year-old civil war.
– More peace talks planned –
It was widely seen as an attempt to disrupt UN-brokered peace talks that took place the following month which to the anger of Fateh al-Sham were supported by its former Islamist rebel ally Ahrar al-Sham.
UN envoy Staffan de Mistura has called a new round of talks for March 23.
Fateh al-Sham has been repeatedly bombed in its northwestern stronghold this year, not only by the Syrian army and its Russian ally but also by a US-led coalition battling IS in both Syria and Iraq.
The rift over the UN-brokered talks between the rebels and the government has also seen deadly clashes between the jihadists and their former Islamist rebel allies.
The two groups had together seized virtually all of the northwestern province of Idlib but are now vying for territorial control.
Bomb attacks are rare in Damascus, a stronghold of the regime of President Bashar al-Assad.
The Syrian capital is sometimes the target of shelling by rebel groups who hold areas on the outskirts.