The volume of classified advertising in U.S. newspapers rose only slightly in May, suggesting the nation's long, steady pace of new hiring has begun to relax, the Conference Board reports.

"All labor market indicators now show that the pace of new hiring has slowed and it is unlikely to rise very sharply again in the next months," said Kenneth Goldstein, an economist for the private business research group."Even the latest employment data show no strong increase or decrease, and May's 5.6 percent unemployment rate matched that of March," he said.

The Conference Board's Help-Wanted Advertising Index, which monitors 51 U.S. newspapers on a monthly basis, reached 160 in May, a mere three points above April's 157 and seven points higher than the year-ago figure of 153. The index is based on 100 registered back in 1967.

According to Goldstein, the prolonged improvement in the labor market has run its course and job growth in the second half of the year will be slower than in the first half of 1988.

The board's figures for May showed that help-wanted advertising volume rose in all but the West South Central region of the United States, which registered a 4.1 percent decline.