Construction of new homes surged 15.7 percent in January to the highest rate in almost two years, the government reported yesterday.

The seasonally adjusted annual rate of housing starts in the first month of 1986 was calculated at 2.08 million -- a 15.7 percent gain over December, the Commerce Department said.

It was the fastest pace of new home construction since February 1984 when the monthly starts indicated homes were being built at the rate 2.21 million a year.

Other government and private statistics released yesterday showed 1985 was a strong year for home construction, only slightly behind 1984. The Commerce Department reported a 0.75 percent decline in private housing starts to 1.74 million from the 1984 figure of 1.75 million.

A private-home construction study by F. W. Dodge showed work began on 1.76 million new homes and apartments, only 0.7 percent less than 1984's sturdy total. Dodge, a division of McGraw-Hill Information Systems Co., said the home-building business strengthened in several regions of the country that had fared poorly in 1984.

"Last year, the long-suffering Northeast bounced back with a surprising 26 percent gain in home building. By contrast, the South, still digesting the leftovers of its earlier boom, started 9 percent fewer housing units in 1985," said George A. Christie, vice president and chief economist of F. W. Dodge.

Deputy White House Press Secretary Larry Speakes hailed the housing starts figures as indicating "tremendous strength" in housing markets. "This is solid evidence that the future of the nation's housing industry -- indeed, the entire economy -- is solid," he said.

Commerce figures showed single-family home starts gained the most ground in January, rising 24.5 percent, to 1.35 million, the highest level since February 1984.

Building permits issued during January remained virtually unchanged. The seasonally adjusted annual rate for the month was 1,870,000, compared with 1.873,000 in December. That figure represents a 14 percent increase over the January 1985 figure of 1,635,000.

The figures compiled by the Commerce Department's bureau of the census said permits for single-family homes increased 11 percent last month. The seasonally adjusted annual rate was 1.08 million, compared with 978,000 in December.

But that gain was offset by a 14 percent drop in permits for buildings with five or more residential units, which fell from a December level of 772,000 to 662,000 in January.

Economists greeted the news as evidence of growing optimism in the economy and an indication, with mortgage rates hovering around 10.5 percent, that more people are finding it is once again possible to own their own homes.

"It's an awfully good start for 1986," commented James Christian, chief economist with the U.S. League of Savings Institutions. "The slippage, and there wasn't much, in multi-family construction just was overwhelmed by the big gains in single-family construction," he said. "I think the single-family sector is certainly going to be stronger" in 1986, Christian added.