The number of planned layoffs at U.S. firms rose 6 percent in July, marking the third straight month of increased layoffs, though downsizing activity appears to be slowing, a report on Wednesday showed.

Employers announced 41,676 planned job cuts last month, up from 39,358 in June, according to the report from global outplacement consultancy Challenger, Gray & Christmas, Inc.

Job losses have increased every month since falling to a seven-year low of 38,326 in April.

Although job cuts have risen in each of the past three months, the increases are so slight and the monthly totals so low when compared to recent years, that the trend in no way suggests a reversal of the significant slowdown in job-cut activity witnessed over the past year, John Challenger, chief executive officer of Challenger, Gray & Christmas, said in a statement.

Overall, employers have announced 339,353 job cuts since the start of 2010, or 64 percent below the 944,048 layoffs announced in the first seven months of 2009.

The July total is 57 percent lower than the 97,373 job cuts announced at the same time last year.

The government and non-profit sector has continued to struggle even as manufacturing and other parts of the economy showed signs of recovery. For the fourth time this year, it was the leading job-cut sector in July, with plans to cut 7,193 jobs, up from 5,306 in June.

The pharmaceutical industry, the second-largest job cutter, announced 37,010 job cuts, 30 percent fewer than at this point last year.

(Reporting by Edith Honan; editing by Leslie Adler)