The state is out with a mixed jobs report showing Massachusetts gained 5,100 jobs in September, even as the unemployment rate crept up two-tenths of a point to 6.5 percent.

The federal Bureau of Labor Statistics also revised downward its previous estimate of job losses in the state during August 2012, from 4,800 to 3,500.

The state office of Labor and Workforce Development said the September jobless rate — which is based on a monthly sampling of households — climbed to 6.5 percent from 6.3 percent in the previous month. The rate has gone up by half a point since June.

The increase of 5,100 jobs in September is based on a separate survey of employers. It comes after three consecutive months of slow or negative job growth in Massachusetts.