Sales of new homes fell in June for the third consecutive month, marking the probable end of the spring housing boom that had been the strongest sector in an otherwise sluggish economy, analysts said yesterday.

The decline in sales since March was attributed to problems in the oil-battered Southwest, the recent rise in interest rates and higher prices of homes in the Northeast due to previous strong demand. Sales of new one-family houses dropped 9.9 percent last month and were 24 percent lower than the rate for March, the Commerce Department reported yesterday.

The housing market had been the economy's one bright spot, economists said. Lower oil prices and interest rates early this year had held the promise of a rebound in economic activity and of further gains in construction and housing-related jobs. But economic growth has slowed from the first quarter, and now housing sales have stalled from the extraordinarily high levels of the spring.

Many of the employment gains in the past few months have been in home building and construction and in related industries such as finance, real estate and insurance.

Economists said housing sales have not completely collapsed, but have reached a more moderate, sustainable level after furious activity in the spring induced by sharply lower interest rates.

Economists said they expect sales to continue relatively strongly through the end of the year at a rate slightly higher than in June, which would make sales about 5 percent higher in 1986 than in 1985.

"I think that peak in March was a little bit out of line with the recent trend," said Commerce Undersecretary Robert Ortner. "Now it is back in line with a smoother upward trend . . . and I think the upward trend will continue."

When asked whether the boom in housing has gone bust, Lyle Gramley, chief economist for the Mortgage Bankers Association, said, "I am not prepared to reach this conclusion yet. Anecdotal evidence shows that the demand for houses continues to be quite strong, although the longer this goes on, the less sure I am of my diagnosis."

New-home sales declined in June to a seasonally adjusted annual rate of 703,000, down from 780,000 in May. The rate in June 1985 was 710,000, the Commerce Department said.

Many economists said that the pent-up demand for housing may have been satisfied and some possible home buyers may have been scared off by the rise in interest rates in the past several weeks. The backup of mortgage-loan applications at processing agencies as a result of the frenetic pace of home buying in the spring also was cited by some economists.

The slowdown in sales "is happening for two reasons," said Gopal Ahluwalia, director of research for the National Association of Home Builders. "A rise in interest rates from the April low of 9 1/2 to about 10.8 percent in June," is one reason. "Secondly, there was a significant decline in the first-time buyer market, as well as there is no pent-up demand."

Although interest rates now are much lower than they were a year ago, the current rates of about 10 1/2 percent are still high, Ahluwalia said. "Some parts of the country are facing much more problems, particularly the oil states, where the unemployment is above the national level," he said.

One reason for optimism about continued strong growth in housing is that interest rates are expected to decline in the next few months as the result of shrinking demand for credit in a weakening economy and pressure on the Federal Reserve Board to push down interest rates to spur growth, Gramley said.

"I expect to see mortgage interest rates back in the single digits in the fall," Gramley said.

In a separate report, the Labor Department said that nonfarm business productivity rose 1.7 percent in the second quarter after the 4.3 percent gain in the first quarter.

Productivity gauges worker efficiency by measuring the output of workers per hour of production. High productivity helps keep business costs low.

Nonfarm business productivity increased 2.4 percent between 1948 and 1973, 0.4 percent between 1973 and 1981, and 1 percent from 1981 to 1985, according to the Labor Department.

Manufacturing productivity grew 1.9 percent in the second quarter, after rising 1.4 percent in the first quarter.