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The nation's unemployment rate fell four-tenths of a percent in May, the government said Friday, but the report still signaled the economy may be cooling off.

The decline to 6 percent, from 6.4 percent in April, was tempered by a smaller-than-expected increase in the number of workers added to the nation's non-farm payrolls. The Labor Department said its survey showed new hires up by 191,000, considerably less than most analysts had expected.In Utah, unemployment increased to 3.7 percent in May from 3.5 percent in April, according to Lecia Parks Langston, chief economist for the Utah Department of Employment Security.

"Joblessness has been trending upward since the beginning of the year, but we still see no reason for concern. Utah's job growth remains prenomenally strong, and our historically low unemployment rate has created problems for some employers who are trying to find workers," Langston said.

About 35,000 Utahns were out of work in May, Langston said, some 800 more than in May 1993 when the unemployment rate was 4 percent.

Reaction to the federal unemployment news was muted on Wall Street, which had feared a much higher number of new jobs that could have signaled higher inflation later. Inflation erodes the value of stocks and bonds.

The Dow Jones industrial average was off about 11 points at 3,748 by midmorning. The yield on the 30-year Treasury bond, a barometer of inflation anxiety, was up marginally at 7.34 percent.

Analysts said the report sent mixed signals - the drop in the unemployment rate to the lowest level this year while the number of new hires was considerable smaller than expected.

President Clinton, traveling today in Italy, told reporters: "As all of you know we got some good news from the homefront today. The unemployment rate has dropped a half-percent."

"The decline in joblessness is a tribute to the American people," Clinton said. "I'm very, very encouraged."

The report "points to a moderation of economic activity from the strong gains of late last year and early this year," said Stephen Roach, senior economist with Morgan Stanley & Co. in New York.

"The basic message underneath is that this economy is growing more slowly than before," said Robert G. Dederick, chief economist with the Northern Trust Co. in Chicago. "It is not an economy that has suddenly turned sluggish, but it has lost that vigorous course that it had earlier."

Katharine G. Abraham, commissioner of the Bureau of Labor Statistics, said the unemployment rate has declined seven-tenths of a percent since January. But the increase in the number of new jobs was lower than 260,000 average increase for the previous four months.

As expected, most of the new jobs were in service-related industries, although growth in that sector was slower than in prior months. Abraham said employment in finance, insurance and real estate declined, which she said reflected in part "the impact of rising interest rates on refinancing and home purchases."

The number of retail jobs increased a modest 31,000. Construction employment was up 12,000 after larger gains in March and April. The size of government payrolls declined about 3,000.

The number of factory jobs was down by about 2,000. Abraham said there were "no noteworthy changes" among individual industries.

The report said Americans worked an average 34.9 hours a week during May, up slightly from 34.7 in April. However, the number of factory hours, which had been at a post World War II high, were down slightly to 42.1 hours from 42.2 hours. Overtime also showed a modest declined. Average hourly earnings were up slightly to $11.11 from $11.05.

Jay Goldinger, chief investment strategist for the Los Angeles investment firm Capital Insight, said the increases in hourly wages and the work week should be the only numbers that cause concern for investors.

Even so, he said the report provided an "all clear signal" to the Federal Reserve not to raise interest rates again.

Most economists had expected the report to show job growth continuing at a reasonably healthy clip, while also indicating some cooling in the economy.