Tony Abbott's sister Christine Forster has described the stalled same-sex marriage plebiscite as a "shitty political deal" struck as an agreement between the Liberal Party's conservative and moderate factions.

The Liberal councillor and same-sex marriage advocate made the startlingly frank admission during a heated debate of Sydney City Council on Monday night.

On Tuesday, Ms Forster told Fairfax Media she stood by her comments but stressed she was not suggesting the plebiscite was cooked up in a cross-factional "deal where Tony sat down with Malcolm, or Eric Abetz sat down with Simon Birmingham".

"I'm saying it was a shitty deal because it was. From my point of view, it was a bad deal because I never wanted a plebiscite; I wanted a free vote in Parliament," she said.