The Department of Housing and Urban Development this week proposed spending about $4 billion to start construction of apartments for low- and moderate-income families this year and in 1979.

The program would vastly expand the number of housing units started for such families - from 128,501 in fiscal 1977 to 180,000 this year to 296,700 in fiscal 1979, which starts Oct. 1.

The units would be financed through low-interest mortgage money put up by the Government National Mortgage Association, a HUD agency. Under a so-called "tandem" program GNMA would buy mortgages from private lenders at below-market interest rates (usually 1.5 per cent lower) and resell them at market rates, absorbing the differences as a subsidy.

Hud already has $2.1 billion in budget authority for the program in the current fiscal year and will seek another $2 billion in fiscal 1979.

Most of the mortgage money would be used to entice builders and developers to construct new apartments for low-fsand moderate-income tenants under HUD's Section 8 assisted housing program. The remaining $500,000 would be targeted to finance mortgages for apartment houses for moderate-income people in central cities.

Another HUD request is for $24.7 billion in new budget authority, which, combined with $6.4 billion carried over from the current fiscal year, will allow HUD to provide rental aid in fiscal 1979 for 400,000 units under the Section 8 and public housing programs. By the end of September, the nation will have 3.3 million of such units.

President Carter's budget said the number of families receiving housing assistance is expected to increase from 2.6 million in 1977 to 3.1 million in 1979.