The area's unemployment rate climbed to 3.5 percent in September, its highest level in more than 3 1/2 years, as the number of suburban residents without jobs rose sharply, the D.C. Department of Employment Services announced yesterday.

For the first time in years, the number of private sector jobs in the area -- a key measure of the health of the economy -- declined, by 7,000 jobs over the last 12 months. An unexplained surge in state and local government jobs sent total employment up 5,200 over the year, but it was still a far cry from the mid-1980s, when the area added more than 100,000 jobs a year.

Those numbers came against a backdrop of national economic statistics showing a slowing economy: A survey of purchasing managers pointed to a weaker industrial sector, while business failures and claims for unemployment benefits rose sharply and construction spending fell.

Today, national unemployment statistics are scheduled for release. Normally the local figures are released at the same time, but this month they inadvertently were released a day early.

"As has been the case for the last several months, the local economy in September produced virtually no new jobs," said F. Alexis H. Roberson, director of the employment department, which compiles the job figures with input from the Virginia and Maryland employment agencies.

The unemployment rate for the District was 6.8 percent, nearly 2 percentage points higher than it was at this time last year. The suburban rate was 3.0 percent, 0.6 percentage points higher than it was in September 1989. The number of suburban residents out of work and seeking jobs was up nearly 12,100 over the year, a 26 percent increase. Total unemployment for the area was 77,800.

Because the local figures are not adjusted for seasonal variations, comparisons with the previous month are statistically shaky. It is more useful, experts say, to look at the changes over 12 months.

The metro-area jobless rate is more than a full percentage point higher than its record low of 2.4 percent in December 1989. Since then, several major retail stores have closed, the real estate industry has slowed dramatically, financial institutions have laid off employees and defense contractors have cut back.

But Richard Groner, chief of labor market information for the Department of Employment Services, pointed out that the area rate is still 2 percentage points below the comparable national unemployment rate of 5.5 percent, and remains one of the lowest of any major metropolitan area.

The decline in private-sector employment of 7,000 jobs was the first drop of its kind since at least the 1981-82 recession, Groner said. Though all the figures were not available, he was not sure the private sector shrank even then.

However, he cautioned, in a local work force of 2.4 million people, the changes in employment fall within the survey's statistical margin of error, even though the trend is clearly flat.

"What you've got is an economy that's not doing much," Groner said. "This area is not producing any jobs."

Among national economic statistics released yesterday:

The nation's industrial sector weakened in October, pushing the overall economy into a decline for the first time in nearly eight years, said a closely followed survey of purchasing executives.

The National Association of Purchasing Management's monthly index of economic activity dropped a full percentage point to 43.4 percent in October, its lowest level since it fell to 42.8 percent in December 1982.

Robert Bretz, chairman of the purchasing managers trade group, said that by falling under 44 percent, the index reached the point where it signaled a small decline in the gross national product, the broadest measure of the nation's economic health.

Virtually all the components of the index "confirmed the growing weakness in manufacturing, which was enough to pull the overall economy into slightly negative growth," Bretz said.

The Commerce Department said construction spending sank 2.8 percent in September, its sharpest plunge in more than 10 years. Residential, nonresidential and government construction spending totaled a seasonally adjusted annual rate of $428.7 billion.

That was the lowest dollar level since $423.1 billion was spent in November 1988, and the 2.8 percent decline was the sharpest since spending fell 3.0 percent in January 1982 in the midst of the 1981-82 recession.

Analysts have said declining confidence due to the Persian Gulf crisis has exacerbated an already weakened construction industry. It had been wracked for months by high interest rates, tight lending requirements and, in some areas, high vacancy rates.

The Labor Department said initial claims for state unemployment insurance benefits increased 33,000 to a seasonally adjusted 454,000 for the week ending Oct. 20. The increase was the second large weekly rise in a row. Some analysts regard 400,000 new claims as a sort of recession threshold, and last week's number was considerably higher than that.

The sudden spurt suggests that national labor markets took a turn for the worse sometime in early October, a fact that could be confirmed today when the Labor Department releases figures for last month's unemployment rate and the number of payroll jobs. Analysts expect the unemployment rate rose from September's 5.7 percent level, while payroll employment and the length of the average workweek likely declined.

And U.S. business failures, driven by dramatic increases in the New England and Middle Atlantic states, climbed 14.5 percent in the first nine months of 1990, according to Dun & Bradstreet Corp. Failures in the New England and Middle Atlantic regions combined soared more than 90 percent in the first nine months of the year, the D&B report said.

"Every industry and every state in these two regions reported sharp increases in business failures, reflecting stress throughout the Northeast," said Joseph Duncan, corporate economist and chief statistician for D&B. "In addition to the dramatic increase in the Northeast, failures are up across the United States, signaling weakness in the U.S. economy overall."

Overall, U.S. business failures rose 14.5 percent to 43,836 from 38,296 in the first nine months of 1990, after three years of steady declines.

This article was supplemented by wire service reports.