The continuing decline in mortgage interest rates helped boost housing starts in the first quarter of the year to the highest level since 1978, although starts fell 2.4 percent in March, the Commerce Department reported yesterday.

Housing starts overall during the first three months of the year were 8 percent higher than the comparable period in 1985. Houses were started at an annual rate of 1.95 million units in March. For 10 consecutive months in 1978, the previous high period, houses were started at an annual rate of more than 1.9 million units.

Although the steep slide in interest rates since last summer has been credited with keeping housing starts at such a high level, lower rates don't appear to be helping all sectors. The Commerce Department also reported that businesses plan to spend only 0.9 percent more this year on plant and equipment than last year. By comparison, inflation-adjusted capital spending grew 7.5 percent in 1985 and 15.1 percent in 1984.

The weak business spending plans, caused largely by the slump in the domestic oil industry, suggest that economic growth in the first quarter of the year will be much lower than expected. The preliminary report on gross national product for the first quarter will be issued today.

Many economists have said that the growth in GNP for the first three months will be about 4 percent because of the decline in interest rates and oil prices. However, the problems of the domestic oil industry related to the oil price decline are expected to cause more problems for the economy before benefits result, and first-quarter expectations have been revised downward, economists said.

The housing industry, however, is prospering. The high level of housing starts "is the first visible effect of the drop in interest rates," said Robert Ortner, the Commerce Department's chief economist.

Mortgage interest rates, generally below 10 percent around the country, are at the lowest level in eight years, Ortner said. "Housing will show the strongest growth of any sector of the economy," he added.

"I was a little puzzled by the fact that housing starts went down rather than up," said Lyle Gramley, chief economist for the Mortgage Bankers Association of America. "The anecdotal evidence coming in says housing is booming. I have a feeling the numbers have not caught up with what's going on out there."

Starts of single-family homes increased 0.7 percent in March, while the rates for units in buildings with five units or more declined from 678,000 in February to 649,000, Commerce said.

Building permits, which indicate future housing activity, increased 2 percent in March. Building permits increased sharply in the West, more than offsetting decreases in the South, Northeast and Midwest.

Ortner said that the Commerce report on business spending plans suggested a slowdown in the second half of the year, related in part to uncertainty about when economic activity will improve and how a tax-revision package pending in Congress will affect them. "I think that, as the economy gathers more noticeable strength through the second half, these investment plans may firm up soon," he said.

In another report, the Federal Reserve Board said that U.S. factories, mines and utilities operated at only 79.4 percent of capacity in March, the lowest level since December 1983.

The reason for the rate reduction is a decline in production for U.S. industries, particularly automobiles. The operating rate in the auto industry fell from 85.1 percent in February to 75.7 percent in March as auto makers cut back production to get rid of unsold cars.