Home sales nationwide hit new lows in September, as the housing industry plunged deeper into its longest slump on record.

The National Association of Realtors announced yesterday that sales of existing single-family homes dropped 8.4 percent in September to 2.07 million units, the lowest ever recorded on a per capita basis and the lowest point in the current sales cycle that began in 1978.

The figure was just about half the peak level of 4.06 million homes being sold in November 1978 and about 36 percent below last September's sales of 3.3 million units.

"This housing depression has reached massive proportions, and by every measure is worse than any housing slide since World War II, 5 1/2 times worse," said NAR Chief Economist Jack Carlson.

In addition, things are likely to get even worse before they get better, Carlson predicted, as interest rates stay stubbornly high.

In the Washington area, sales also continue to plummet. Sales of new homes and condominiums dropped 10 percent from August to September and 38 percent from a year earlier, according to Housing Data Reports, local home specialists.

The severity of the local sales slump actually was obscured by the overall September figures, however. A number of condominium conversion projects, on which tenants had put deposits earlier, went to contract in the month, resulting in an unusual 11 percent rise in local condo sales that helped offset a 26 percent decline in sales of other types of homes, Housing Data reported.

New-home construction starts also have fallen precipitously. Last week the Commerce Department announced a drop in starts that virtually assures a postwar record low of about 1 million units in 1981.

NAR's Carlson accused the administration of having a "sacrifice-the-housing-industry" attitude in developing economic policy that he said has exacerbated the housing slump. The Realtors group is calling for more budget cuts, a delay in scheduled tax cuts and loosening of credit by the Federal Reserve Board.

Administration policies are unlikely to change from its reliance on current economic policies to bring interest rates down and stimulate home sales, however.

Philip Winn, Housing and Urban Development assistant secretary for housing, said the administration is using "the only feasible economic policies available to us" to solve the nation's housing crisis, adding that housing "remains one of the top priorities of the Reagan administration."

He added that the administration is "vigorously pursuing" several housing-production alternatives, such as tax incentives, creative-financing options, programs to encourage condominiums and manufactured housing and elimination of red tape. But he rejected looser credit as a solution.

"Talk of quick-fix solutions of unrestrained fiscal and monetary policies to satisfy immediate demand is irresponsible," Winn said.

Asked if the latest bad news on home sales might prompt the Fed to loosen its credit policies, a Fed spokesman replied with an unequivocal "no."

Median home prices over the past year have risen 5 1/2 percent in nominal terms but are 5 1/2 percent lower than a year ago when adjusted for inflation, Carlson said.

When interest rates finally do come down, the unsatisfied demand for housing could result in another buying spree and boom in prices, he added.