The council has also agreed to her using the public land, although it says it has no position on her protest.
Ms Curran said yesterday no homes had yet been found for the women, and she planned to stay where she was.
She is advocating for proper housing for Kylie Taggart (30), who is 26 weeks pregnant, and Amy Stuart (25), both of whom are receiving emergency accommodation in motels.
The Ministry of Social Development has said the women had repeatedly exhibited behaviour that made them unattractive to landlords and many motel owners.
Mr Cull said as a courtesy he had texted Ms Curran and offered the use of a shower at the council buildings.
He said the council did not have a position on the issue, and the same courtesy had been extended to protesters from the Occupy movement in 2011, when portable toilets and electricity were provided.
Council strategy and governance general manager Sandy Graham said the council had in the past granted permission for people to camp in the Octagon for charitable and/or political purposes, provided they were not causing a nuisance.
''Ms Curran informed us over the weekend of her intention to camp in the Octagon.
''We remain in close dialogue with her and have no concerns whatsoever at this stage.''
Ms Curran said she was ''hanging in there for another night,'' despite the cold, and had put up a bigger tent, as the weather was expected to change for the worse.
Ms Curran said there had be no change in the situation with her battle to get the two women housed.
''I'm quite worried about both young women. They're doing it quite hard with all the public attention.''
The women came in for criticism on social media
after some posted publicly available Tenancy Tribunal rulings against them, showing damage to homes and unpaid rent.
Ms Curran said those critics did not know all the circumstances.
''Both women have freely acknowledged they have things in their past that they're not proud of.
''They're trying to turn their lives around.''
