A jump in job cuts in the computer and education sectors drove an increase in layoffs at U.S. firms in June, even as the pace of downsizing in the first half of the year improved overall, a report on Wednesday showed.

Employers announced 39,372 planned job cuts last month, up 8.2 percent from 36,398 in May, according to the report from consultants Challenger, Gray & Christmas, Inc. June's layoffs were also up 4.8 percent from a year ago.

Still, the number of job cuts in the first half of the year was down 8.5 percent from the first six months of 2012.

With the third quarter typically a slow period for downsizing, that puts layoffs on track to see the second-lowest yearly total since 2000, said John Challenger, chief executive officer of Challenger, Gray & Christmas.

"Unless, there is a major shock to the economy in the second half of 2013, we could see layoff activity continue to decline toward pre-2000 levels," Challenger said in a statement.

The report comes ahead of Friday's key U.S. jobs report, which is forecast to show the pace of hiring cooled slightly in June, while the unemployment rate is expected to dip to 7.5 percent.

The computer industry led the increase in layoffs for June, with 10,133 workers losing their jobs. That was followed by the education sector, which cut 5,629 positions.

The aerospace and defense sectors have been hardest hit by the across-the-board government spending cuts known as the sequester that went into effect in March, the report said.

Since the beginning of the year, the sectors have lost 4,366 jobs related to the sequestrations, while the government has cut a further 1,976 employees for that reason.