Proponents of the grant include organised labour, HIV/Aids, youth, aged, faith-based, children and human rights organisations.
The Basic Income Grant Coalition proposes a monthly grant that would be paid by the state to everyone legally resident in South Africa, regardless of age, income, family status, or other factors.
The BIG is one way of giving effect to the right to social security, guaranteed by the Constitution.
Supporters of the grant have recommended that it be set at R100/month at first, rising with inflation.
Opening the conference, which will continue today, Molefe Tsele, secretary-general of the South African Council of Churches said, "We are calling for a BIG solution to alleviate poverty”.
The conference began with the government's ten-year review, which documents the scope of poverty.
Yasmin Dada-Jones from the Office of the Presidency outlined the South African government's commitment to eradicating the poverty, which is debilitating families and communities in the country.
Dada-Jones stated, "We have a dual economy and government wants to create equity and expel exclusion".
More than half of all South Africans, including two out of three children, live in poverty.
Nearly 12-million of the poorest South Africans live in households that currently receive no social assistance, and although South Africa is by no means a poor country, it has one of the highest rates of inequality in the world.
In a recently launched book on the BIG, researchers stressed the strong connections between poverty reduction, improved nutrition, health and education and labour market participation.
There is a strong link between severe inequality and low rates of economic growth.