The output of the nation's factories, mines and utilities, which declined sharply because of cold weather and energy shortages in January and early February, recovered later last month, the Federal Reserve Board reported yesterday.

The nation's central bank said that after a revised 0.8 per cent decline in January, industrial production rose 1 per cent during February.

The recovery in production supports Carter administration contentions that the severe winter would not have a lasting impact on the economic recovery and that growth would rebound smartly from winter doldrums.

Some economists and members of Congress had argued that the bad winter would throw the economy off course and that the $16 billion program proposed by President Carter and revised slightly by Congress to pick up the lagging recovery would be negated by the effects of weather and fuel shortages.

But the Federal Reserve Board reported yesterday that the January decline and "weather-related production losses early in (February) were more than offset later by sizable output gains in many industries."

The recovery in production also parallels the Labor Department report earlier this month that the unemployment rate rose only slightly in February and the number of persons with jobs grew.

When manufacturing output falls, as in January, layoffs result and when output recovers, employers recall workers.

The Fed initially reported the January output decline as 1 per cent but revised it to 0.8 per cent on the basis of further information.

The central bank said that the "factory workweek in February lengthened considerably from the average in January, and the warmer weather put less pressure on fuel supplies available to industry."

As a result, nearly all categories of production increased. Only the output of durable consumer goods -- almost all automobiles -- fell.

Nondurable consumer products, such as textiles, rose 0.9 per cent and business equipment output jumped 1 per cent. The output of materials, such as metals, rose 1.2 per cent in February. But despite this large increase, the Fed noted that it was not enough to offset the decline in production of materials during January.

The agency noted that automobiles were assembled at an annual rate of 8.2 million vehicles, a 3.5 per cent drop from January. Most other consumer durable goods like appliances rose, but not enough to offset the decline in cars. Overall, consumer durable goods production fell 0.4 per cent.