The nation’s bleak employment picture dimmed in September as private-sector hiring weakened and the economy lost a net 95,000 jobs over the month.

The Labor Department said Friday that the unemployment rate last month remained at 9.6 percent, but that reflected a stagnant labor force in which people did not enter or return to the labor market to look for work. In what may be a more meaningful indicator this time, a broader measure of unemployed and underemployed workers, including part-timers who can’t find full-time work, rose to 17.1 percent last month from 16.7 percent in August.