Construction of new housing in February leaped 93 percent from a year ago to a seasonally adjusted annual rate of 1.756 million units, persuading some observers that the housing industry is in recovery and worrying others that depleted supplies will not meet demand and, worse, they'll cost more, too.

The increase, a 2.9 percent gain from the previous month, surprised many economists who had predicted a drop from the 1.7 million starts in January, which, in turn, was 33.4 percent higher than starts in December, according to figures released yesterday by the Commerce Department.

Although industry leaders were cheered by the increase in starts, some were concerned that the continued demand for new homes may overwhelm short inventories of building materials and the capacity of builders not yet geared up for full production after years of recession.

Washington-area developers report sharp increases in the cost of construction materials during the first two months of this year, as high as 10 to 25 percent for lumber and drywall.

The National Association of Home Builders, the industry's largest trade group, has forecast that materials prices nationwide will increase 5 to 10 percent during 1983.

New homes "are on the edge of affordability now," and increases in home prices caused by rises in material costs could jeopardize the housing recovery, said NAHB economist Bob Sheehan.

"There'll be problems if the starts stay at the 1.7 million" annual rate, Sheehan said, but the NAHB is predicting the number of starts for all of 1983 will be lower, at 1.45 million.

Building permits issued last month totaled 1.493 million, about the same as the number issued in January. The figure is high enough to keep housing starts at the February level for "at least another two months" before construction begins to drop, NAHB President Harry Pryde said.

The cost of a new home may rise 5 to 8 percent from last December to April, Mortgage Bankers Association President James M. Wooten said yesterday.

"The numbers substantiate an across-the-board recovery for housing. And particularly encouraging is the number of starts in the multifamily area," Wooten said.

Apartment construction is responsible for the increase in housing starts, with starts on units in buildings with two or more apartments rising by more than 25 percent. The rise indicates that "the private sector is moving back into the rental housing and condominium markets," Wooten said.

Starts of single-family houses declined 8 percent last month, the Commerce Department report shows.

"As long as interest rates are reasonably stable, I don't see house prices going up enough to have an unfavorable impact on sales," Wooten said.

He predicted that interest rates would stay around their present levels for the next six months. Increases in recent weeks have brought rates on fixed-rate conventional and on FHA loans to slightly more than 13 percent.

NAHB President Pryde also warned that mortgage interest rates "must decline further and stay down" to avoid a "flash-in-the-pan recovery like the one experienced in 1980." Housing starts rose dramatically between May 1980 and January 1981 in the wake of sharply reduced interest rates, then collapsed when interest rates rose again.