Four search and rescue officers are in talks with the protesters on the ground and the climbers.
The protest is delaying the setting up of part of the White Night arts festival event, because police have cordoned off footpaths and the cafe area around the centre.
Centre security were alerted to the women, Hannah Patchett, 22, and Katherine Woskett, 25, climbing the 162-metre spire about 3.30am on Friday.
The pair unfurled a "#LetThemStay" banner in time for the peak-hour commuter rush.
Arts centre staff endorsed a statement from their union, the Media Entertainment and Arts Alliance, in support of the protest.
The MEAA said the protest drew attention "to the human rights abuses being committed in our name in Australia's offshore detention system, in particular at Manus Island and Nauru".
Ms Patchett and Ms Woskett also suspended themselves from the Yarra Bend Road overpass on the Eastern Freeway on Thursday, February 11.
The action is the latest in a campaign against 267 asylum seekers - including 91 children - who are in the country for medical treatment, being sent to Nauru.
Protest spokeswoman Gaye Demanuele said Ms Patchett and Ms Woskett, experienced climbers, were prepared to stay up the spire for as long as they could.
"They believe the risks they are taking are nothing compared to the risks asylum seekers take to seek asylum and safety," Ms Demanuele said.
Former immigration minister Scott Morrison criticised the women's protest.
He questioned why the pair did not make such a display when there were 2000 children in detention at the last election.
"Maybe they've only developed climbing skills more recently," he told Radio 3AW in Melbourne.
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