Housing starts decreased in June for the fourth consecutive month as builders, concerned about mortgage rate hikes, worked at the slowest pace in nearly three years, the Commerce Department said yesterday.

The government estimated new home construction in June stood at an annual rate of 1.59 million homes, down 0.7 percent from May. Starts of single-family homes dropped 2.4 percent, to 1.092 million. Those figures are seasonally adjusted.

On the positive side, the department reported that the issuance of building permits rose 1.4 percent, to 1.5 million.

The June level was the lowest for housing starts since August 1984. Not since 1981 have they dropped for four straight months.

"The housing market appears to be settling down following the upturn in mortgage rates experienced in April and May," said James Fischer of Nashville, Tenn., president of the National Association of Home Builders.

"Mortgage rates have begun to recede and further declines should spur single-family starts this summer and fall," predicted Robert Ortner, the Commerce Department's undersecretary for economic affairs.

Mortgage rates shot up more than 1.5 percentage points between April and late May when financial markets began worrying about inflation and the prospects for a U.S. trade war with Japan.

Mortgage rates since have declined about 0.5 of a percentage point, but the run-up has made many builders more cautious.

Builders have begun work on 831,400 homes, 10.8 percent fewer than at this point in 1986.

That puts them on track to start more than 1.6 million homes, down from last year's 1.805 million but about what many economists predicted for 1987.

James Christian, senior economist for the U.S. League of Savings Institutions, said analysts expected fewer home starts this year because the economy was not supposed to do as well as in 1986, which was abnormally good.

He said the housing industry in general appears to have weathered the mortgage rate jump by turning to alternatives: adjustable-rate mortgages instead of fixed-rates, existing homes instead of new ones.