Mr Dunham said the board was concerned demand for emergency services appeared to be increasing every year, and that was the first priority.
The ministry had put the health board on performance watch - which meant it worked with the board to look at the issues it faced and the actions it needed to take to "reduce [its] exposure", he said.
"We meet on a monthly basis."
He said the forecasted budget for the 2016-2017 year was still to be signed off.
"However we are planning to have a surplus at year end."
Mr Dunham said one example of the cost cutting measures was getting control of the use of locum doctors.
The ministry also has the health board on watch for other performance issues - including key performance indicators emergency department waiting times and smoking advice in the primary sector.