Ms King said the Ministry of Health's mistake had only emerged publicly after a Labour researcher noticed one line in a Treasury report on the ministry's finances: "I think [a cover-up] started off in the Ministry of Health, but has moved on to the minister."
The controversy relates to a multi-million dollar project to refit the ministry's Wellington head office. That was approved by the Government in 2014, after the ministry said it could use forecast cash reserves to meet the $24 million cost.
However, the ministry later learnt its financial team had miscalculated, and there wasn't enough money to complete the project.
Before the last Budget it put its hand out to the Government for $18 million in order to finish the job.
In a statement, Mr Chuah said he acknowledged that unacceptable mistakes had been made, and when it was brought to his attention he commissioned Pricewaterhouse Coopers to undertake an independent review to establish what occurred, and ensure it would not happen again.
He said the project has now been completed without the need for any additional Government funding.
"The forecasting error does not affect health service funding and relates only to the Ministry of Health's accommodation operating costs."
The funding needed for the refit was being secured by spreading the cost over the life of the building's lease, which would be "fiscally neutral".
"We anticipate the project will be completed within budget by the end of this year," Mr Chuah said in the statement.
This morning, Ms King said the claim the lease would be "fiscally neutral" seemed extremely suspect.
"If it is spread out over the life of the project, someone is paying for it. And I would say it is being paid for by increased rent to the landlord over the period of the lease - that is money that comes out of operation."
"I can't understand why the Auditor General wasn't asked to look at what happened...we wouldn't have known that there was a Pricewaterhouse Coopers report. To me, this whole thing stinks of a cover-up."
On his way into a caucus meeting, Dr Coleman said Mr Chuah had learnt some lessons, but was doing a good job helping deliver better health services.
The cost had been structured into the lease.
"But look, that was always the agreement that Treasury had with the Ministry of Health, and they weren't meant to come back and ask for that $18 million. So, to be honest I think you have overblown this a little bit, but there's no question they made a forecasting error, they have got a new CFO, they have got new personnel there and new processes.
"It was not good financial management, absolutely. And they have been slammed for it and they have taken responsibility...but, in terms of the director general, he is absolutely the right man for the job. It is not a resignation level offence."
Mr Chuah was confirmed as director general and chief executive of the ministry in March last year. A qualified chartered accountant, he had been acting in the role since November 2013.
