Construction of new housing, fueled by declining mortgage interest rates, jumped a hefty 17.5 percent last month, the government reported yesterday.

Reagan administration officials and most housing industry leaders immediately applauded the figures as a strong indicator of a healthy economy and a harbinger of good times for housing construction and sales over the next few months.

Tempering the enthusiasm for the report was that the substantial December percentage increase was based on the relatively low number of new homes started in November.

Presidential spokesman Larry Speakes called the increase "another sign of a booming economy. Anyone who doubts that 1986 will be a good year clearly is not abreast of the continuing good economic news."

Commerce Secretary Malcolm Baldrige said the December starts -- lifting the year-end total to 1.73 million, just shy of the 1984 figure of 1.75 million -- shows that "demand for housing remains strong.

"The number of households in the first-time buying years continues to grow," Baldrige said. "Existing home sales climbed 11 percent last year, indicating an active market. Continued growth in employment and consumer incomes, and lower mortgage rates, currently under 11 percent, should raise housing activity this year."

Warren Lasko, executive vice president of the Mortgage Bankers Association of America, said, "With interest rates down, we've been expecting housing starts and housing sales to go up, and indeed they have. Interest rates came down at the end of October and housing sales were up in November, and builders now appear to be making their move with new housing starts."

James Christian, chief economist for the U.S. League of Savings Institutions, noted that the housing industry, which in the past has experienced sharp yearly fluctuations in volume, has now had three almost identical years in a row, with 1.7 million starts in 1983, 1.75 million in 1984 and 1.73 million last year.

Most housing analysts predict that about the same number will be built again this year, perhaps slightly fewer.

"Those numbers are right on demand in demographic terms," he said. "There's a whole lot to cheer about."

The Commerce Department report pegged December housing starts at a seasonally adjusted annual rate of 1.84 million, the highest figure since April and up sharply over the revised November rate of 1.57 million. The November figure was partly reduced by a hurricane in the South.

With the onslaught of cold weather, the actual number of housing starts last month totaled 114,700, but that number was still markedly better than the 98,900 in December 1984. Such figures are then adjusted to compute annual rates.

The December increase was generated largely by a boost in construction in the sometimes volatile multi-family housing sector.

That factor led one economist, Thomas Lawler of the Federal National Mortgage Association, to suggest that the figures may overstate the overall health of the industry.

Economist Christian also warned that "the financial markets will jump on the housing-start increase as a sign of a strengthening economy, but probably they really shouldn't."

Lasko said the increase in multi-family starts was a reaction to a more predictable tax outlook, at least for the next year. Starts of multi-family units dropped last fall as tax reform measures pending in Congress threatened the outlook for tax benefits for construction of rental housing.

"There has been a reprieve on tax reform for at least the next 12 months with continued good tax inducements for rental housing," Lasko said.

"The numbers also reflect a new trend, with lenders and developers turning their attention from office construction to rental housing construction," he said.

The seasonally adjusted rate for housing units authorized by building permits, an indicator of housing starts to come, also increased sharply in December, up from 1,661,000 in November to 1,844,000, the highest figure since February 1984.