According to Christian Aid partners many people are concerned about the impact his death may have on the progress of Sudan's already fragile north-south peace process.
Dr Garang, who led the Sudan People's Liberation Movement (SPLM), died on Saturday in a helicopter crash.
Rioting broke out in the capital, Khartoum and the main centers of Juba, Malakal, Kosti and Port Sudan. After a brief calm, there are now reports of renewed disturbances in and around Khartoum.
However, the full implications of his death are as yet unknown. Christian Aid is monitoring the situation closely and will support partners who are building on the Comprehensive Peace Agreement, signed in 2004.
Three weeks ago Dr Garang - seen by many as a instrumental in the peace process - was sworn in as the vice president of Sudan.
In Darfur, there were hopes that Dr Garang could play an important role in negotiating peace in the region.
Christian Aid's partner, the New Sudan Council of Churches has reported that his death has caused 'profound shock and deep sorrow'.
In a statement they added: 'His death has hit us all like a thunderbolt, coming at a time when our hopes were at an all time high and when we were set for the reconstruction of our nation.'