The administration yesterday announced proposed cutbacks of $20.3 billion in new Federal loan guarantees to be made in 1982, which are part of the September budget package announced by President Reagan. The cuts, which include some scaling back in government-backed mortgage financing, brought immediate complaints from housing industry spokesmen.

Despite yesterday's statement on the loan guarantees, the Office of Management and Budget is still waiting for agencies to come forward with detailed legislative proposals on the loan package. However, it should be possible to make the bulk of the savings administratively, without congressional approval, Lawrence Kudlow of the Office of Management and Budget told reporters yesterday. Other elements of the September package have still to be agreed on within the administration.

The bulk of the saving in credit guarantees would come from a $16 billion reduction in new guarantee commitments for the Government National Mortgage Association (Ginnie Mae). The quasi-governmental corporation sells government guaranteed securities, backed by pooled mortgages from the Federal Home Administration, the Veterans Administration and the Farmers Home Administration.

Kudlow said the cutback from $64 billion of new commitments for Ginnie Mae would not hurt the housing industry, and that the overall credit reduction proposal was designed to "provide the financial market equivalent of a $20 billion reduction in budget outlays -- since loan guarantees are typically converted into direct spending not recorded as part of the official budget."

However, spokesmen for the Mortage Bankers Association of America strongly challenged this. The Ginnie Mae change, which would amount to a 30 percent reduction from the $68.25 billion of new 1982 commitments authorized by Congress, "will further damage an already depressed housing market" and will have no effect at all on either on-budget or off-budget outlays, they said.

Four major programs would be cut back under yesterday's proposals. Apart from Ginnie Mae, the others are:

* Rural Electrification and Telephone Revolving Fund: proposed $1 billion reduction from $5.2 billion current level.

* Export-Import Bank guarantee and insurance program: $1.2 billion from $8.2 billion.

* Small Business Administration: $1 billion from $5 billion.

Cuts in 10 small programs will yield a further $1.09 billion in reductions in credit guarantees in fiscal 1982, OMB said. These include the Farmers Home Administration ($300 million proposed cut) and section 108 community development ($250 million proposed cut).