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Chief executive Chris Fleming confirmed the Dunedin unit would cost $14.8 million - not the $11 million made public.
To make up $3.2 million of the shortfall, the board would dip into a special $7.3 million maintenance fund, but it planned to ask for more maintenance money, Mr Fleming said.
The remainder would come from normal operational funding.
The maintenance money was allocated by the Government to keep the crumbling facility operational in the years leading up to the rebuild.
In 2015, a special $22.5 million financial package was announced for a new ICU, gastroenterology unit, audiology unit, and maintenance.
Construction of the ICU began in June after long holdups for design and budget approval.
The new unit includes a new high-dependency unit and will have 18 beds.
The inadequacy of the existing ICU has been in the spotlight recently because of cardiac surgery cancellations caused by a lack of ICU beds.
The board expects the new unit will relieve some pressure, but it is unclear how many of the 18 beds will be resourced ICU beds.
Each ICU bed required a full-time nurse.
It is likely to have a relatively short lifespan, as it will only be needed until the new hospital is built.
Deputy commissioner Richard Thomson said the cost increase proved the commissioner team was willing to listen to doctors and allow more spending than expected.
''We have approved a redevelopment that is greater in scope than that $11 million will pay for.''
The ''tight market'' in Dunedin for building work was a factor in the increase.
Mr Fleming said he was preparing to apply for more maintenance money.
''Yes [part of the ICU budget is] initially coming out of deferred maintenance, but the reality is deferred maintenance is going to be an even bigger demand than we expected.
''We're busy pulling together how we're going to keep this place going over that time period until the rebuild's completed.
''The number's going to be much bigger, and we're going to be working with the ministry on that,'' Mr Fleming said.