New Jersey’s unemployment rate reached 9.8% in September, up from 9.6% in August, as officials estimate that the state lost roughly 12,700 nonfarm wage and salary employment positions.

The 9.8% jobless rate for New Jersey mirrors the national average. The state lost about 12,000 private-sector jobs last month and about 700 public sector positions, according to its  Department of Labor and Workforce Development.

In the Northeast, New Jersey is second only to Rhode Island for high unemployment. Rhode Island’s jobless rate rose to 13% last month, up from 12.8% in August.

New Jersey officials are seeking to deal with job losses while readjusting the state’s fiscal 2010 budget. Gov. Jon ­Corzine last week announced $205 million of budget savings and spending cuts to help match spending to underperforming revenue. First-quarter tax revenue came in $190 million below budget estimates, a decrease of 3.1%.

In addition, the governor ordered his cabinet to find another $200 million of budget reductions by Dec. 1 to make up for sluggish tax collections.

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