The promise, which is not specified in the party's election platform, was unveiled by Health Minister David Wilson. He said the measure would bring spending on administration down from 4.83 per cent of the health budget to four per cent.
Wilson released few other details at his announcement and couldn't say how many jobs could be affected, but said the money saved would be put into patient care.
In an interview later, Dexter said no jobs would be lost as a result of reducing administration costs.
"We are not talking about job cuts at all," he said. "This is all about using the money in the envelope to do better management."
Wilson said the promise follows the government's work carried out after a February 2012 report by consulting firm Ernst & Young outlined ways of saving money in the health care system.
In response to that report, the government said it would merge administrative services such as payroll and laundry and cut as many as 128 jobs, including 11 to 20 vice-president and director positions at the province's 10 health boards.
Wilson said Monday as many as 18 vice-president positions have been eliminated or merged so far. The NDP did not return a request later seeking clarification of that figure.
The NDP's promise comes after the Liberals committed to slashing the number of health boards from 10 to two in a move that party says would save $13 million. The Progressive Conservatives say they would cut the number of boards to three and implement all of the recommendations of the Ernst & Young report for savings of $60 million.
The NDP has said it would not cut the number of health boards.
Liberal Leader Stephen McNeil said the NDP announcement was a surprise given that it wasn't contained in the party's platform.
"Very clearly they recognize Nova Scotians have been listening to what we've been saying," said McNeil.
But McNeil said the announced reduction would have to come more quickly in order to avoid affecting frontline health care with anticipated federal changes to the funding formula for health care in 2015.
Progressive Conservative Leader Jamie Baillie said the NDP's change would be minimal.
"They defend the system of 10 health authorities that we have now and try to convince us that they are running efficiently," said Baillie.
Earlier Monday, McNeil said his party would spend an estimated $6.5 million annually on a graduate training program for businesses if he wins the Oct. 8 election. He said some details of the program would be worked out with small business owners, but he added it would provide payroll incentives to businesses that provide a minimum of 12 months of employment and training to new university and college graduates.
Dexter also announced that the NDP would implement a diabetes wellness plan aimed at preventing, screening, detecting and treating the disease.
Note to readers: This is a corrected story. A previous version said the Ernst & Young report was done in March 2012.