"I pay tributes to our brave soldiers," Dr Singh said in his condolence message to the bereaved families.
A Lt Colonel was among the five army personnel killed on Tuesday when their 32-member convoy came under attack in Gurmuck in the volatile state of Jonglei, South Sudan.
Four others were injured in the attack.
There are around 2,200 Indian army personnel comprising two battalions, one based in Jonglei and the other in Malakkal, Upper Nile, on the border with Sudan.
Since South Sudan got independence in July 2011, it has witnessed ethnic strife, with Pibor county, the main base of UN peacekeeping force, being the centre of much of the violence.
India is a major contributor to UN peacekeeping forces around the world and has suffered losses in the past