Civil society organisations described Johannesburg's Central Methodist Church, where thousands of migrants have taken shelter, as unsustainable.
"The present situation that faces those living in the church is not sustainable," Aids Law Project director Mark Heywood said on Tuesday.
Heywood was reading from a statement signed by more than 30 civil society organisations including the Congress of South African Trade Unions, Amnesty International, Human Rights Watch, the Centre for the Study of Violence and Reconciliation, the South African Council of Churches (SACC) and the Treatment Action Campaign.
Heywood said the situation had become untenable because of health risks posed by overcrowding.
The situation was made worse in July with the arrests of 300 people sleeping on the streets around the church.
This had resulted in more people wanting to stay inside, in relative safety from the police, Heywood said.
"This place is not a solution but I don't know where there is a solution," said a Zimbabwean refugee staying in the church, Evans Kuntonda.
"Most of the [Zimbabwean] people would like to go home. Central Methodist Church is not an ideal place. But we don't have a choice," he said.
SACC general secretary Eddie Makue described the overcrowding at the church as South Africa's "shame".
"We are ashamed by the overcrowding here because if we were responsive to your needs you would not have overcrowding here."
Heywood said that closing the church was not an option.
"If the church were to be closed, as has been threatened [allegedly by the government], the people who need its support would not miraculously evaporate.
"Refugees would be dispersed and forced underground into places where they would be less accessible and in greater danger of health and human rights violations," he said.
Heywood and Makue said a solution needed to be found that respected the dignity of those in the church.
Makue said South Africans should apologise for the way their marginalised had been treated.
"We are deeply concerned that the human dignity of people is being trampled on the way it has been with the people of the church." — Sapa