Dr Jonathan Coleman said in a statement that the bungle was before his time as Minister of Health, but he had made it clear to Mr Chuah that the handling of the issue was unacceptable.
"The Ministry undertook an independent review, and as a result it has implemented a number of changes to strengthen its financial processes. There has also been some changes to finance personnel at the Ministry."
Mr Chuah said he acknowledged that unacceptable mistakes had been made.
"As Director-General I take responsibility for fixing these mistakes. When the issue was brought to my attention I immediately commissioned Pricewaterhouse Coopers to undertake an independent review to establish what occurred and ensure it doesn't 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.
The PwC review found no single cause for the forecasting error, but highlighted financial capability issues within the Ministry, including financial forecasting.
"The ministry accepts all of PwC's recommendations and is working to implement them. We are also implementing a new finance function which elevates the position of CFO to the second tier to directly report to me," Mr Chuah said.
"A senior Treasury official is acting in this position while recruitment of a permanent CFO is underway."
One News reported that Treasury papers showed it described the funding miscalculation as "serious financial mismanagement", and believed that, had Treasury been consulted, it would have picked up the shortfall.
Treasury's chief executive, Gabriel Makhlouf, sent a letter to Mr Chuah -- then the Ministry of Health's acting director general -- in which he said: "The new bid for funding brings into question the governance and financial management practices of the Ministry."
Labour's health spokeswoman Annette King told One News that Mr Chuah should resign over the blunder.
"It is quite clear in the Treasury documents that have been released, they have said they would not approve it ... I would expect the Director-General to offer his resignation."
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.