South African minister Jeff Radebe said this on Monday, urging the heavily-criticised Nigerian government to investigate the "tragedy".
(READ MORE: Nigeria church building collapses, kills 67 South Africans)
The September 12 disaster in the church compound of popular preacher T.B. Joshua, which Radebe says killed 84 South Africans from visiting church groups, has opened up a diplomatic rift between the two African economic heavyweights.
South Africans are angry at what they see as the Nigerian government dragging its feet on launching an investigation into the collapse, which occurred when three storeys were being added to the two-storey building, and for not reacting more quickly to help those trapped under the rubble.
Nigerian emergency services said the total death toll was 86 and have refused to comment on nationalities of those who died.
Nigerian President Goodluck Jonathan visited the site on Saturday, offering his condolences to Joshua, who has been the focus of South Africans anger after he described the victims as "martyrs of faith" on his Facebook page.
Joshua and his supporters say the collapse was an "attack" somehow linked to a mysterious aircraft they say flew over the building before it fell down.
Analysts say Nigeria's megachurch leaders are so influential that few politicians dare upset them, especially just before a national election, which Nigeria is due to hold in five months.
Radebe spent much of his news conference congratulating the work of South African emergency workers for the "biggest evacuation by the air force since the dawn of democracy".
He did not mention the efforts of Nigerian emergency services or the church but said Nigeria was carrying out an investigation, although Jonathan has not announced any probe.
"We are keenly awaiting as a South African government the investigation that is being conducted by the Nigerian government so that we get to the bottom of the cause of ... this national disaster," Radebe said.
South Africa's media has been scathing of Joshua and the Nigerian government, especially after the Nigerian emergency services said the church had failed to cooperate and had blocked rescuers' access to the site.
"Blood on their hands" was the front page headline of South Africa's Sunday Times. Many Nigerians have also been critical.
"I very much hope that the South African government keeps up the pressure on the Nigerian authorities. What happened must not be allowed to be treated in a typical Nigerian fashion," popular Nigerian columnist Tolu Ogunlesi wrote on Monday.
"Had it only been Nigerian lives lost in the collapsed building, the fuss would have been less. We would have moved on quicker. Because life in this country isn’t worth very much."
Joshua's church draws thousands of followers from all over Africa and other parts of the world, attracted by assertions that he and his "wise men" can cure almost any affliction by "casting out demons" they say are responsible for everything from madness and HIV/AIDS to normally irreparable spine damage.
The regular influx of visitors from abroad for church services that can last up to a week creates demand for accommodation that the church's own guesthouse has been unable to meet, and often spills over into local hotels.