Initial jobless claims for state unemployment compensation slipped back slightly in the week ended Oct. 9, but were still at their third-highest level since the recession began, the Labor Department said yesterday.

The total of 685,000 initial claims was down by only 11,000 from the previous week and 18,000 from the high of 703,000 reached in the week ending Sept. 18. The continued high level of jobless claims suggests that unemployment will not decline next month from the post World War II peak of 10.1 percent reached in September, economist Alan Greenspan said.

Claims have now been running at close to 700,000 for four consecutive weeks and above 600,000 for nine weeks. Many economists fear that the jobless rate may climb still higher this month from the September level.

The October tally will be reported on Nov. 5, just after the congressional elections. Despite recent declines in interest rates and the stock market rally, there is little sign as yet of any recovery in the economy.

Commerce Secretary Malcolm Baldrige predicted this week that the economy will be "flat" or show only a small increase in real terms in the current quarter, after growing a scant 0.8 percent in the third quarter.

Unemployment typically lags behind changes in production as firms first increase their output with the existing work force and only later begin to take on more workers.

Thus, the unemployment rate may continue to climb even after the economy begins to turn around.

Greenspan said the Labor Department report suggests that unemployment among skilled workers has continued to increase since September, with the layoff rate apparently stabilizing, but at a high rate. Rehires are running well below the level of initial claims, Greenspan said. Yesterday's report suggests that there may be a further drop in payroll employment this month, experts say.