Housing starts dropped 2.9 percent last month, provoking fears that rising mortgage interest rates may choke off the recent home-buying spree.

The number of new houses on which work was begun last month fell to an annual rate of 1.74 million from 1.79 million in May, the peak for the past 3 1/2 years. Although the number of housing starts was lower than in May, it was 92 percent higher than in June 1982.

"Housing starts appear to be leveling off," said Commerce Secretary Malcolm Baldrige. "Unless the recent increase in mortgage interest rates is reversed, some retrenchment in starts could be in the offing.

"The high level of interest rates is a direct result of the large budget deficits--actual and prospective," Baldrige continued. "If the deficit is not reduced, federal financing demands will begin to crowd the interest-sensitive sectors out of the credit markets, jeopardizing the prospects for further recovery of residential construction."

"Rising mortgage interest rates threaten to choke off the current housing-led economic recovery," said Harry Pryde, president of the National Association of Homebuilders. "This could go down as the shortest housing recovery in postwar history. It started last October and could end by late summer. We expect the current high level of housing production to drop sharply this year unless the current upturn in interest rates is reversed."

However, other economists said that, although the housing figures dropped, they still were strong compared to the slump during the previous three years.

Housing starts "were ridiculously high in May," said Michael Carliner, chief housing forecaster for Chase Econometrics. "To think of this as a decline rather than continued strength is misstating the situation." But Carliner cautioned that rising interest rates could lead to a decline in starts from current levels during the remainder of the year. "Mortgage rates are already beginning to affect sales," he said.

Since the beginning of June, mortgage interest rates have risen a full percentage point to about 13 percent, and several economists yesterday said they expect rates to climb to about 14 percent by the end of the summer.

"The rapid improvement in the first six months of the year probably won't be sustained through the second half of the year," said James M. Wooten, president of the Mortgage Bankers Association of America. "The housing recovery, however, is remaining strong and continues to lead the economic recovery. The starts in permits this month were probably on stream before interest rates started their increase."

The Commerce Department said that the overall decrease in housing starts was led by a 7.1 percent decline in starts of single-family homes. Single-family homes were started at a revised annual rate in May of 1.187 million compared with 1.103 million last month.

Starts of buildings with five or more units stayed virtually the same during June as in May, at 510,000, the Commerce Department said. However, starts of buildings with two, three or four units increased by 36.7 percent from 98,000 to 134,000.

Permits for future construction improved for the third straight month to an annual rate of 1.745 million, the highest level in 4 1/2 years and a 7 percent increase from an annual rate of 1.635 million in May.