WASHINGTON (AP) _ Housing construction rose a moderate 2.4 percent in July, the government reported Wednesday, but economists warned that rising mortgage rates could make the two-month housing rebound a brief one.

The Commerce Department said new homes and apartments were being built at a seasonally adjusted annual rate of 1.49 million units last month after advancing 4.4 percent in June.

Housing starts had dropped a sharp 12.1 percent in May to the slowest pace in three years, and rising mortgage rates were blamed.

The June-July rebound was attributed to stabilized mortgage rates, but last week the Federal Reserve boosted the discount rate, the interest it charges for loans to member banks.

This move was widely interpreted as the opening salvo in a renewed battle by the central bank to drive up interest rates to fight inflation. As a consequence, a variety of other interest rates, including the banks' prime lending rate and mortgage rates have moved higher.

Fixed-rate mortgages rose to 10.57 percent by the end of last week and analysts predicted mortgages would soon top 11 percent.

''I believe we have seen the peak for housing starts this year as rising interest rates cut into sales,'' said Richard Peach, an economist with the Mortgage Bankers Association.

David Seiders, chief economist of the National Association of Home Builders, said his organization was so concerned by the Fed's credit- tightening moves that he asked Federal Reserve Chairman Alan Greenspan in a letter for ''a more even-handed approach.''

''Clearly, the Fed views the housing industry and other interest rate- sensitive sectors of the economy as being sacrificial lambs,'' Seiders said.

Sales of homes and other high-priced items usually are the first to fall off when the Federal Reserve tries to dampen borrowing by raising interest rates.

Michael Sumichrast, an economist and publisher of a construction industry newsletter, said that if mortgage rates climb to 11.5 percent or higher, it would spell disaster for the housing industry.

He said home sales already have been hurt by big price increases in many parts of the country.

''I don't think you can sell houses at 11.5 percent to 12 percent mortgage rates in this market because of the price increases,'' Sumichrast said.

Analysts say another worrisome sign is that housing permits, considered a good barometer of future activity, fell in July by 5.4 percent to an annual rate of 1.41 million units. It was the biggest permit decline since January.

James Christian, chief economist of the U.S. League of Savings Institutions, said the drop in housing permits probably reflects builders' fears of rising mortgage rates.

He said the impact of higher rates should be moderated by a consumer shift toward adjustable rate mortgages, which carry a lower initial rate.

The July increase stemmed from a big jump in starts of multi-family construction, which offset a small decline in single-family units.

Single-family homes were being built at an annual rate of 1.08 million units last month, down 0.8 percent from the June level.

Construction of multi-family units shot up 12.1 percent to an annual rate of 409,000 units following a 6.2 percent decline in June.

The multi-family sector has been depressed for nearly two years because of the adverse effects of the 1986 tax law on real estate investment, but some analysts said the steep decline in apartment construction finally may have bottomed out.

By region, housing starts were strongest in the Middle West, climbing by 12.1 percent to an annual rate of 296,000 units. Construction rose 9.2 percent in the Northeast to an annual rate of 262,000 units.

Construction fell 3.2 percent in the West to an annual rate of 368,000 units, and it slumped 1.2 percent in the South to a rate of 563,000 units.

For the first seven months of 1988, housing starts have been running 10.6 percent below the level of the same period in 1987.