The government reported yesterday that housing starts declined in February while the nation's industrial output rose sluggishly, providing two possible signs that economic growth finally may be beginning to slow.

Analysts cautioned that both figures were distorted by the impact of bad weather. Nevertheless, the statistics were sufficiently lackluster to indicate there has been some slowing from last quarter's heady pace.

The figures on housing left the number of starts in February at an annual rate of 1.41 million -- down from a 1.67 million rate in January and well below December's 2.06 million pace.

Industrial production rose a sluggish 0.3 percent, following a period of no growth in January. In the final three months of 1978, industrial output posted increases ranging from 0.6 percent to 0.8 percent a month.

Analysts were not certain how big a part the bad weather played in depressing either figure. Economists cautioned, however, that because of this and other factors, they may not get a really accurate reading until spring.

Still, Kenneth Biederman, economist for the Federal Home Loan Bank Board, said there was little doubt that in the case of housing, at least, there had been a genuine slowdown from the final months of 1978.

Moreover, the February figures did not yet reflect the recent steps by the government to cut back the impact of six-month money market certificates -- a move that is expected to crimp housing even more.

Michael Sumichrast, economist for the National Association of Home Builders, said the February figure shows "the beginning of a decline through 1980. We are out of the 2 million start rate for another year or more."

The sluggish performance of industrial production was spread throughout virtually every sector of the economy. Output of consumer goods remained unchanged from January's levels, in part because of a dip in auto production.

Nevertheless, output of business equipment continued robust in February, indicating there still is no sign of relief from the economic overheating in that sector.

Many analysts fret that the pace of activity in the industrial sector is adding seriously to inflation pressures. Part of the adminstration's economic review next week is expected to touch on this development.

The decline in housing starts was concentrated in the category of single-family dwellings. Starts of multi-family units dipped less sharply. And regions hit hard by bad weather suffered particularly steep declines.

The number of new building permits sought -- a bellweather of future housing starts -- rose 3 percent in February. But it remained at a relatively low annual rate of 1.3 million units -- suggesting little prospects of a big rebound.

The new figures came as Alfred E. Kahn, President Carter's chief inflation fighter, repeated earlier warnings that Carter's wage-price program will be a failure if there isn't progress by early summer.

In a speech before the National Newspaper Association, Kahn said, "I will regard it as a sign of failure if by something like the beginning of summer we don't see signs of tapering" in the inflation rate.

Barry Bosworth, director of the Council on Wage and Price Stability, had made similar comments last week.

The rise in industrial production brought the overall index to 151.2 percent of its 1967 average. Industrial output in February was 8.6 percent above its level of a year ago.

Among the various components of the index, production of materials rose by 0.3 percent in February, following an 0.1 percent dip the previous month, while output of construction supplies rose 0.1 percent -- half January's pace.

Production of intermediate products jumped 0.2 percent last month, compared to a rise of 0.6 percent in January.

The conference Carter has ordered Monday of his economic and energy advisers is primarily to discuss what to do about the energy situation, but aides said yesterday it may touch as well on serveral key economic areas.

The first of these is how to bolster the anti-inflation program, which is being strained by the sharper-than-expected price increases that have come in the past few months.

Policymarkers are considering several measures to tighten the current wage-price guidelines, along with other proposals intended to deal with inflation problems in particular sectors of the economy.