“By so doing, we will not only be putting to rest all the speculations, we will be preventing similar tragedies waiting to happen,” spokesman Benson Upah said.
“Similarly, a shoddy investigation is capable of compromising the image of Nigeria.”
Around 115 people were killed and dozens trapped when the multi-storey guest house attached to the church collapsed on September 12.
On Sunday, government said the number of South Africans killed in the tragedy had been revised from 84 to 80.
“We have established that four of the remains are not South African citizens. Three are citizens of Zimbabwe and another one is from the Democratic Republic of Congo,” spokeswoman Phumla Williams said.
Minister in the Presidency Jeff Radebe said on Sunday that 62 of the South Africans killed had been identified to date, the same figure announced last Wednesday.
The NLC said the victims’ relatives deserved to know the truth.
It called on the Nigerian government to empower the national emergency management agency to improve its response capacity.
“We commiserate with the families of the victims, [the] majority of whom are our South African brothers and sisters,” the NLC said.