Younan Abdulla, who was 28, was taking part in a sit-in over the long running dispute between the church's land and buildings committee and an what's been described as an illegally-convened rival church committee backed by the government.
The protest, which took place last weekend, at the Evangelical School in Omduran was attended by school teacher and church members.
The school is part of Khartoum Bahri Evangelical Church which has had difficulties with the authorities.
According to religious freedom group Christian Solidarity Worldwide, the church elder was involved in an altercation when members of the rival church committee arrived with knives, machetes, and firearms
Mr Abdulla and another man were stabbed and transferred to a nearby hospital, where he died from his injuries several hours later.
He is survived by his wife and two children.
CSW's Chief Executive Mervyn Thomas said: "We extend our heartfelt condolences to the family of Elder Younan Abdulla and to the Evangelical Church in Omdurman.
"We are calling for a thorough and speedy investigation into the circumstances surrounding his death and for all those responsible to be held to account.
"We urge the Ministry of Guidance and Religious Endowments to authorise the legitimate SEPC committee to administrate on behalf of the denomination.
"We also call for an end to the policy of targeting places of worship for demolition and erasing the Christian presence from the country. This violates Sudan's obligations under its constitution and international treaties to which it is party.
"We urge the African Union, the European Union, UK and US governments to hold the Sudanese government to account in order to ensure justice for Sudan's Christian community in general and for the family of Elder Abdulla in particular."