At least 20 people were killed and dozens injured in a suicide bombing at the Mar Elias Church in Syria's capital Damascus on Sunday, health authorities and security sources said.

It was the first suicide bombing in Damascus since Bashar al-Assad was toppled by an Islamist-led rebel insurgency in December.

Syria's interior ministry said the suicide bomber was a member of Islamic State. He entered the church, opened fire and then detonated his explosive vest, a ministry statement added.

A security source, speaking on condition of anonymity, said two men were involved in the attack, including the one who blew himself up.

A priest at the church said the congregation had heard shooting outside before two people entered with explosive belts and detonated them during the Sunday Mass.

Islamic State has been behind several attempted attacks on churches in Syria since Assad's fall, but this was the first to succeed, another security source told Reuters.

Syria's state news agency cited the health ministry as saying that 52 people were also injured in the blast.

Syrian President Ahmed al-Sharaa, who led the offensive against Assad before taking over in January for a transitional phase, has repeatedly said he will protect minorities. (Reuters)