The nation's industrial output rose moderately last month, reversing an abrupt decline in August that had some analysts worried the economy might be entering a prolonged slump-period.

New figures from the Federal Reserve Board showed production in factories, mines and utilities up 0.4 per cent in September, off setting a similar decline in the previous month. The August dip had been the first since last January's cold spell.

The board estimated that about a third of the overall jump reflected a rebound from strike activity earlier. Labor disputes in mid- and late-summer had slut down facilities in the coal and copper industries.

Nevertheless, the remaining portion of the increase was widespread enough to lead analysts to speculate it may be the start of a general pickup in the economy following the late-summer slowdown.

Meanwhile, separately, a top White House official reiterated the administration's unhappiness over the Fed's recent monetary tightening, and - according to an Associated Press report - pointedly noted its chairman's term is expiring.

The wire service quoted Stuart Eizenstadt, the President's chief domestic adviser, as saying "when you are pushing stimulating fiscal policy, and someone is pulling on monetary policy, the obvious effects of stimulus get dampened."

It said Eizenstadt also reminded a meeting of the Democratic Party's finance committee that Arthur F. Burns' term as chairman will expire early next year, giving Carter an opportunity to name a new chairman.

At the same session, Charles L. Schultze, the President's chief economist, was quoted as conceding that business investment in new plant and equipment currently is too low to enable the administration to meet its goals.

The report on industrial production was regarded as moderately encouraging. Economists have blamed some of the recent sluggishness on an adjustment in business inventories. Some say that shift has now run its course.

The rebound in production accompanied a resumption in September of job-growth in the industrial sector of the economy. Industry payrolls had fallen off visibly in August, but last month they rose respectably again.

Yesterday's report showed gins in every sector of the economy. Output rose by 0.3 per cent in consumer goods, durable goods, business equipment and intermediate products, and by 0.2 per cent is non-durable goods.

The largest gains were in two less-visible categories: Production of materials jumped 0.6 per cent in September, while output of construction supplies gained by 0.5 per cent.

The September report brought overall industrial output to 6.3 per cent above its level a year ago. The index now stands at 138.8 per cent of its 1967 average.