The nation's industrial output rebounded in March after slowing dramatically in the two previous months, the government reported yesterday-bolstering earlier indications that the economy is overheating.

Figures published by the Federal Reserve Board showed production levels of the nation's factories, mines and utilities rose a substantial 0.8 percent over the month after remaining unchanged during January and February.

Although part of the rise reflected a rebound from the effects of bad weather last winter, the increase was large and widespread enough to indicate a continuing boom in the industrial sector of the economy.

Economists both in and outside the administration have expressed fears that this rapid overheating is causing excess demand that is helping to pull prices up more sharply than they otherwise would rise.

President Carter's top economic advisers have been considering new steps to help cool the overheating some, but Carter indicated through aides yesterday he plans to have no part of any such moves.

The march rise in output was concentrated in production of consumer durables-big-ticket items such as automobiles and refrigerators. Production of these items rose 1.9 percent over the month, up from 0.1 percent before.

Output of basic materials also rose sharply, climbing 1 percent in March after declining in the two previous months. Increases in other major sectors of the economy were moderate last month.

The March increase brought over all production levels to a point 8 percent above that of a year ago. The index now totals 152.2 percent of its 1967 average. Output of basic materials stands at 10.5 percent above a year ago.

The March rise marked the strongest increase in industrial production since December's jump of 0.9 percent. The index had been moderately strong throughout the second half of 1978, and is expected to continue robust.

Yesterday's figures showed a sharp rebound in automobile production. Auto assemblies rose by about 6 percent last month to a new annual rate of 9.4 million units. Car production slipped earlier this year.

Most of the sluggishness in the January and February figures stemmed from bad weather that gripped much of the nation, including heavy snows and local storms that kept many workers from their jobs.

Industrial production is considered a key economic indicator because it provides the broadest monthly measure of output by basic industries. A more comprehensive measure, the gross national product, is scheduled to come out next week. CAPTION: Chart, no caption