A man who was killed by two Islamic State gunmen during Sunday service at a church in Istanbul had gone into the building while out for a walk, his cousin said on Monday, while authorities said the attack could have been deadlier if not for a jammed weapon.

Authorities said the masked gunmen entered the building and shot dead a 52-year old Turkish citizen, Tuncer Murat Cihan, at the Italian Santa Maria Catholic Church in the Sariyer district. The attackers, one from Tajikistan and another from Russia, have been detained, along with 51 others after the attack.

Murat Cihan, the victim's cousin, said his relative had no political or religious connections and lived "in his own world".

"He got out for a walk and went to the church and this unfortunate thing happened to him there," he told reporters at his cousin's funeral.

Sariyer's district mayor Sukru Genc was cited by local media as saying two shots were fired by the perpetrators before one of their guns jammed, adding it was not clear whether the attackers planned to kill more people.

CCTV footage verified by Reuters shows the two gunmen waiting briefly in an entrance hall at the church, before following a man inside. Another angle shows the attackers shooting the man walking in ahead of them.

Istanbul Mayor Ekrem Imamoglu said the Polish consul general was also inside the church with his family during the attack. On Sunday, President Tayyip Erdogan had called the Polish diplomat, along with the church's priest, to offer his condolences.

Footage from inside the church on Monday showed bullet holes on the side of a pew, as well as another in a wall. Candles were lit inside, with the building surrounded by police.

Islamic State claimed the attack in a statement on Telegram, saying it was in response to calls by its leaders to target Jews and Christians.

Tuncer, the victim, was Alevi, a religious minority whose beliefs draw on Shi'ite Muslim, Sufi and Anatolian folk traditions, and a funeral was held for him at a cemevi, the Alevi places of worship.