The issue was brought to light by Cope earlier this year, when it said section 6 of the bill was discriminatory.
The section allowed Department of Home Affairs marriage officers to be exempt from performing civil unions.
Officers could object to performing the union on the ground of conscience, religion and belief to solemnising a civil union between people of the same sex - and to be exempted from officiating at such marriages.
Of the 1 131 marriage officers at the Department of Home Affairs branches, 421 were exempt from performing civil unions.
The bill was adopted by the portfolio committee on home affairs, and a "B Bill" will be put forth, and thereafter a date will be set to debate the bill in the National Assembly.
Triangle Project health and support services manager Sharon Cox said this was a big win. It meant a lot for the LGBTI+ community, she said.
She said while many people chose not be to married, those who did deserved the right not to be discriminated against.
“This was not about the right to marry, but about the right to equality. If we look at section 6, what made it difficult was there are a few marriage officers available to marry people. In a research process that was undertaken it was shown that 29% of officers nationwide are able to marry people.”
Cox said that of this small number, many were exempt.
“Home Affairs officers prepared to marry (same sex) people are not evenly distributed. For instance, in rural areas like Witzenberg there is no one who will marry you. You have to travel over 100km to be wed. It’s a blatant prejudice.
“You will not have marriage officers denying people from different races or different religions or of different ages. You will never find officers denying people on those grounds. Their religious beliefs should not be shaping rules.”