WASHINGTON — A wave of census layoffs cut the nation's payrolls in June for the first time in six months, but private employers added a modest number of jobs.

That caused the unemployment rate to fall to 9.5 percent, its lowest level in almost a year.

Employers cut 125,000 jobs last month, the most since October, the Labor Department said this morning. The loss was driven by the end of 225,000 temporary census jobs.

Businesses added a net total of 83,000 workers, an improvement from May. But that's also below March and April totals.

The unemployment rate dropped to the lowest level since July 2009. But it fell because 652,000 people gave up on their job searches and left the labor force. People who are no longer looking for work aren't counted as unemployed.

The nation still has 7.9 million fewer private payroll jobs than it did when the recession began. It takes about 100,000 new jobs a month to keep up with population growth.