The Reagan administration's plan to slash government loan-guarantee programs could cripple the Federal Housing Administration and Veterans Administration loan programs that have enabled millions of Americans to become homeowners, housing industry groups predicted yesterday.

Home building, mortgage banking and savings and loan officials all warned that the already depressed housing industry will be hurt more if the administration cuts the long-established home-loan programs.

The National Association of Homebuilders predicted housing starts could fall by as much as 250,000 a year if the administration cuts the loan guarantee authority of the Government National Mortgage Association, better known as Ginnie Mae.

Other housing industry economists said the immediate effect probably will not be that great because the housing market is already severely depressed. Mortgage interest rates are so high that few buyers can afford a mortagage of any kind, so cutting back government mortgage guarantees will not hurt much right now, they argued.

Sales of new houses plunged to an annual rate of 362,000 units last month, down 41 percent in the last year, the government reported yesterday.

Nationwide, 34,000 new homes were sold during August, and the backlog of unsold new houses climbed to 300,000 -- a 10-month supply at current sales levels.

One of the chief sources of home mortgage money is Ginnie Mae, which raises funds that are used to make government-guaranteed loans through the FHA and VA programs.

President Reagan last week vowed to cut government-guaranteed loans by $20 billion in fiscal 1982, which starts today. Borrowers utilizing federal loan guarantees are crowding other borrowers out of the market and forcing up interest rates, administration economists have said.

When the Office of Management and Budget announces details of the loan-guarantee cuts next week, Ginnie Mae is expected to be the biggest loser.

The GNMA is the largest of the government loan guarantee programs, OMB officials pointed out. "If we're serious about reducing the government's claim on the credit markets, there's no way we can do that without cutting GNMA," an OMB spokesman said.

Other guaranteed loans are made by the Farmers Home Administration, Rural Electrification Administration, Small Business Administration, Federal Maritime Administration and the Export-Import Bank.

The $20 billion reduction in loan guarantees promised by Reagan would cut total new loan commitments in fiscal 1982 from about $79.6 billion to about $59 million. The actual amount of government-guaranteed loans made would be less than that.

Of the original $79.6 billion in 1982 commitments, Ginnie Mae originally was projected to claim almost $65 billion for mortgages. Because the housing market is so depressed, the GNMA probably will be able to make no more than $50 billion in loans.

OMB officials won't say how much the GNMA's loan guarantee level will be cut, but housing industry executives expect a ceiling of $40 billion to $45 billion on the GNMA in fiscal 1982 and further reductions in 1983 and 1984.

The home builders' trade association estimates such a ceiling could chop another quarter-million housing starts a year off new home production.

The GNMA last year provided funds for 72 percent of the loans made under the most familiar, unsubsidized FHA loan program, and about 45 percent of the money for VA loans.

"GNMA has been a very important source of funds for us. I would hope they wouldn't cut it too much," said Richard Lawton, chairman of Washington-Lee Savings & Loan of McLean and president of the National Savings and Loan League.