By Patrick McGeehan

The unemployment rates for New York City and State shot up in August as the rapidly spiraling economic downturn left more people without jobs, the state’s Department of Labor said on Thursday.

The city’s unemployment rate rose to 5.8 percent from 5 percent in July — the largest monthly increase in more than 30 years — as about 5,200 private-sector jobs were eliminated, the department reported. Many of the layoffs came in the tumbling financial sector, which is one of the city’s biggest employers and the provider of nearly one-fourth of its annual wages and salaries.

In the last 12 months, employment in the financial realm has declined by 5,300 jobs, according to James Brown, an analyst with the Labor Department. Some of those losses resulted from the collapse of the Bear Stearns investment bank in March. But many of the cutbacks at that firm and others on Wall Street still have not shown up in the official statistics.

For example, the August totals do not include the 1,500 layoffs that Lehman Brothers had planned to make before it was forced into a bankruptcy filing on Monday. Lehman, which employed more than 25,000 people, has sold its main trading operations to Barclays Capital, a London-based firm, but it is not known how many of the 10,000 employees of those operations will keep their jobs. American International Group, the Manhattan-based insurance giant, was on the brink of failure before receiving an $85 billion lifeline from the federal government this week.

“Although the crises at Lehman Brothers and A.I.G. appear to be working out so as to avoid immediate large-scale layoffs, the continued financial-sector turmoil guarantees that job losses on Wall Street will climb rapidly over the next few months,” Mr. Brown said.

Despite the current deterioration in the job market, the city still had about 31,000 more jobs last month than it had in August 2007, when the unemployment rate was 5.3 percent, according to the report. Most of that job growth has come in the fields of education, health care, trade and transportation, and leisure and hospitality.

“Most of the professional business industries such as law firms lost a small number of jobs in August, but all in all, New York City has still yet to see any significant impact from the turmoil on Wall Street,” said Barbara Denham, chief economist for Eastern Consolidated, a real estate investment firm.

“This will undoubtedly change in the next few months, but the job losses from Lehman Brothers’ bankruptcy and Bank of America’s purchase of Merrill Lynch may not hit the job numbers until November or later,” Ms. Denham said. “While New York City’s economy remains well diversified in health care and private education, the problems on Wall Street will likely spill over into the business travel industry, which would affect hotels, restaurants and entertainment.”

The jobless rates for the city and the state were lower than the national unemployment rate, which jumped to 6.1 percent last month, according to the Labor Department.

Statewide, the jobless rate also rose to 5.8 percent, from 5.2 percent in July. That was the largest monthly increase in the state’s rate since January 1991, said Peter A. Neenan, director of the department’s division of research. Still, the department reported that the state added 3,000 private-sector jobs in August.

“New York State’s labor market indicators reported mixed signals in August,” Mr. Neenan said.