The new cuts will most seriously affect administrative staff and trades workers.
The HHC budget plan was to be released Tuesday. It calls for 2,400 job cuts in the next four years. That includes 1,000 in the next year through attrition and layoffs.
In 2009, HHC had a 39,000 work force.
The HHC also may close health clinics and combine some outpatient services.
It needs to close a $1.2 billion gap in next year's budget.