However, he insisted they would work with all stakeholders in the public sector, including unions.
The public sector wage bill has been increasing over the years and stands at over R500 billion.
But Cosatu warned it would not allow retrenchments in the public sector.
Mchunu said the issue of the public sector wage bill was just one of the hiccups they would encounter.
Mchunu said they would work with the unions.
“There is no way I can walk away from the unions. Not only must we work closely... we must forge common objectives,” said Mchunu.
The National Treasury said in the Budget in February it would start the process of allowing for early retirement and it would not penalise those who made this choice.
This would allow for natural attrition, which formed part of government plans to cut the wage bill.
Mchunu said he wanted stability in the public service, as this had been lacking in the sector for some time.
“I know from what we have been observing, we do need greater stability in the public service. There are many disruptions in the form of strikes and work stoppages, and it affects governance. The public service is an important vehicle for government to fulfil its mission,” said Mchunu.
Mchunu was one of the new ministers who took office after President Cyril Ramaphosa appointed the new Cabinet.