Last month, a council report suggested it was in such bad condition it was a risk to safety and would have to be dismantled so it could be determined how to restore it.
But councillors were worried that, once in bits, it might not be possible to put it back together so deferred any decision for further reports.
The council's committee of the whole was told this week by recreation manager Eric van der Spek additional information suggested work on the fountain was not as urgent as engineers had believed, although it was impossible to know for sure until it was dismantled.
Options for the fountain would continue to be investigated and the community consulted through a reserve management plan.
One of those involved in an earlier refurbishment of the fountain, Dunedin monumentalist Ian Bingham, said the fountain had been reassembled in the 1990s after a second renewal of pipes. A strong epoxy glue and dowells were used.
Cutting through the joints would seriously weaken the whole structure, which he believed was quite stable.
Another Dunedin monumentalist, Marcus Wainwright, who had worked for the council recently on monumental work, said external support for the fountain could be used to secure it while options were looked at.
He also expressed concerns about dismantling the fountain.
The fountain was given by Oamaru timber merchant John Craig in 1912 and is a major feature at the entrance to the gardens.
Extensive work was carried out on it in 1990 after parts wore out and vandals had damaged it over the years.
However, the fountain leaked, was turned off during the 1990s and has not flowed since.
Dismantling the fountain had been estimated to cost $20,000, with restoration and reassembly to working order $60,000 to $100,000. A bequest had been made to the gardens for work on the fountain.
The fountain is listed by the New Zealand Historic Places Trust as category 2. A conservation report in 2001 recommended dismantling the structure, repairing broken pieces, repairing and restoring pipes and the water supply, reassembling the structure and restoring the pool at its base to its original design.
