A month-long rise in a key unemployment indicator has caused some economists to fear that the pace of the economic decline may be worsening.

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The level of initial claims for unemployment benefits--one of the best early indicators of what is happening in the economy--has marched steadily upward since mid-February. For the week ended March 20, it reached 623,000, the highest level since the recession began except for one week in early January when holiday closings of claim offices distorted the figures.

The release this morning of the latest weekly figures for initial claims may add to the fragmentary evidence that the recession is deepening again.

Private economic forecasters, and those in the Reagan administration, generally agree there is no sign of an economic upturn yet. But most have been saying, as Robert G. Dederick, assistant secretary of Commerce for economic affairs, did yesterday, that "the recession pretty well has blown itself out."

Dederick told reporters that industrial production probably fell in March after a rebound the month before from the sharp, weather-related plunge in January. And he added, "The true trough of the recession may not yet be here."

However, there was no suggestion from Dederick that the rate of decline might be getting worse again, and that is what some economists fear may be happening. One of them, Alan Greenspan of Townsend-Greenspan & Co., said cautiously that while the unemployment claims figures are too erratic to draw such a conclusion as yet, "that is the right question to be asking."

Explained Greenspan, "The current level of interest rates, by suppressing consumption and making inventories excessive relative to consumption, is the root of the problem. Until rates fall, it is difficult to envision any significant pickup in activity."

Dederick expects the slump to end sometime this quarter to be followed by a moderately paced recovery--real growth at a 4 percent to 5 percent annual rate--in the second half of the year even if interest rates do not fall.

But without a drop of about 4 percentage points in long-term interest rates later this year, he said, the recovery could be "limping" and "unsustainable"

The Commerce economist said action by Congress to see that federal budget deficits decline in future years likely would produce such a drop.

If rates stay high, Dederick said he still doesn't "think the danger is a further downward spiral" for economic activity.

Current efforts by business to reduce inventories eventually will run their course unless there is a collapse in final demand, that is, in total purchases by consumers, business and governments for consumption and investment. "Final demand has held up. It has not crumbled," he said.

In his own view, Dederick continued, "this could be one of the best of the post-war recoveries. . . . We really have laid the groundwork for what could be a strong long-run recovery" because of the progress in cutting inflation.

Dederick said the "underlying inflation rate may be down to 6 percent," certainly somewhere between 6 percent and 7 percent.

The moderate sort of recovery he expects, however, would still leave unemployment at or above the 9 percent level, the record for the post-war period. Asked if it would be below that level at the end of the year, he replied, "It's very iffy."