The Carter administration has quietly promised civil rights groups to seek passage of a major civil rights bill in this Congress.

The legislation would greatly enhance the government's enforcement powers under the basic federal Fair Housing Act, which Congress passed in 1968.

That act strictly forbids racial discrimination in the sale or rental of most housing -- but it also limits the help the government can give to victims of such discrimination. The result is that the act has been mainly a declaration of good intentions that have gone largely unenforced.

The forthcoming bill, which seeks to change that, has drawn opposition from some segments of the mortgage and insurance industries and the nation's real estate industry. They opposed a version on which a House Judiciary subcommittee held hearings last year.

Under the 1968 law, a person who thinks he or she has suffered discrimination can either go to court on his own, a process that tends to be both slow and costly, or turn for help to the Department of Housing and Urban Development. But all HUD can do for him, if it decides he is in the right, is try to mediate in his behalf. It cannot order anyone to do anything.

Under the bill, whose House sponsors last year were Reps. Don Edwards (D-Calif.), chairman of the Judiciary subcommittee on civil and constitutional rights, and Robert F. Drinan (D-Mass.), HUD's power would be expanded so that it could adjudicate cases brought to it, and the secretary could order remedies where discrimination was found. These orders could only be issued after trial-like hearings, and could be appealed to the courts.

But in effect the bill would be creating within the executive branch a special minicourt system to hear housing discrimination cases, just as the National Labor Relations Board hears charges of labor law violations.

Civil rights groups have tried several times in the last 15 years to win similar adjudicative power for the Equal Employment Opportunity Commission in the field of job discrimination. These attempts all failed. The two most important helped provoke the great Senate civil rights filibusters of 1964 and 1972.

Before the 1972 legislation, EEOC had only the power to conciliate complaints that HUD now has. That legislation gave EEOC, as a compromise, the added power not to decide cases, but to carry them into the courts on its own. The agency thus can now represent complainants.

Congressional and administration aides say the housing bill would empower the secretary to hear cases involving exclusionary practices of local government as well as actions by private parties.

The courts have held that the 1968 law applies to governmental as well as commercial activity. The new bill would give the secretary further power to help enforce that 1968 law, its drafters say.

HUD already has the power to cut off the federal community development funds of local governments that refuse to make satisfactory provision for low-income housing within their borders. That power has also been pretty much unused, however.

HUD's fair housing enforcement program has been a disappointment to Secretary Patricia Roberts Harris. She recently reorganized it, and former D.C. City Council chairman and unsuccessful mayoral candidate Sterling Tucker has taken over as here new assistant secretary in charge of fair housing.

The Leadership Conference on Civil Rights, a confederation of most of the major civil rights organizations in the country, decided last November to put a new fair housing bill at the top of its legislative wish list in this Congress.

The chairman of the leadership conference, Clarence Mitchell, sent a letter to James McIntyre, director of the Office of Management and Budget, and Stuart Eizenstat, presidential assistant for domestic affairs, asking that the president "give this legislation priority on his calendar and urge its adoption in his State of the Union message."

Harris and Drew Days, assistant attorney general for civil rights, had already testified in support of the Edwards-Drinan bill at the hearings held by Edwards' subcommittee last spring.

But "We are sure you understand that a far more active effort by the Carter administration is needed if the bill is to be enacted into law," Mitchell wrote.

Carter's response came in the lengthy written State of the Union message he sent Congress as a supplement to the one he delivered in person. Halfway through its 50 pages were these paragraphs:

"We need to correct a weakness in an existing civil rights law. Title VIII of the Civil Rights Act of 1968, which prohibits discrimination in housing, remains largely an empty promise because of the lack of an adequate enforcement mechanism.

"I will soon propose to the Congress that this problem be alleviated by providing the Department of Housing and Urban Development with cease-and-desist powers. That department, which now investigates and makes findings upon individual complaints, would then be able to enjoin further discriminatory acts and to direct and appropriate remedy. My administration will work with the Congress to see that this proposal is given prompt and favorable consideration."