Nearing the end of assembling what he called "a Cabinet of great quality," President-elect Ronald Reagan yesterday named the first woman, the first black and the first southerner to the group, along with an interior secretary who vowed to fight conservationists who try to "lock up" the nation's mineral resources.

The four new nominees appeared -- without at a Mayflower Hotel news conference dominated by questioning of Secretary of State-designate Alexander M. Haig jr., who urged the Senate to clear his nomination by the time Reagan is inaugurated on Jan. 20. Haig had been named earlier by Reagan.

Introduced to the nation yesterday by transition press secretary James Brady were Reagan's choices for:

Secretary of interior: James G. Watt, 42, of Englewood, Colo., the president and chief attorney of the Mountain States Legal Foundation, which has fought environmental groups on a wide range of issues relating to development of the West.

Secretary of housing and urban development: Samuel R. Pierce Jr., 58, of Long Island, a former state judge and general counsel of the Treasury Department who is the highest-ranking black appointee of the new administration.

Secretary of energy: James B. Edwards, the 53-year-old former governor of South Carolina and a practicing oral surgeon in Charleston, S.C. Edwards, the first southerner in the Cabinet, said he had not discussed with Reagan that president-elect's campaign promise to abolish the Energy Department.

Ambassador to the United Nations: Jeane J. Kirkpatrick, 54, of Bethesda, a Georgetown University political scientist and resident scholar at the American Enterprise Institute. Kirkpatrick, the first woman in a Cabinet-rank position in the new administration, supported Reagan for the presidency but reaffirmed her Democratic Party affiliation at the news conference.

Yesterday's anouncements -- all of them confirming previous forecasts -- left only three Cabinet-rank positions unfilled. Some, if not all, of the remaining appointees are to be announced today.

One announcement, according to transition sources, is the selection of John R. Block, the Illinois commissioner of agriculture, as secretary of agriculture. Reagan confirmed the choice in a curbside chat with reporters in California, then said, "I don't want to jump the gun" on the formal announcement.

The other remaining posts are secretary of education and special trade respresentative. The education post has been the source of endless pulling and tugging. The newest name in speculation is Ed Aguirre, a commissioner of U.S. education in the Ford administration who now is superintendent of schools in Santa Clara County, Calif.

Aguirre would be the first Hispanic in the Cabinet, but sources said there was potential problem in his appointment because he was a member of the Citizens Committee for a Cabinet Department of Education and testified in 1977 in favor of its creation. Reagan has pledged to abolish the department because he says it interferes with local control of schools.

The job of trade representative -- once held by Robert S. Strauss and now filled by former Florida governor Reubin Askew -- is one of several posts reportedly available to outgoing Republican National Chairman Bill Brock. But transition officials reportedly are undecided whether to give the post the Cabinet rank it enjoyed in the Carter administration.

In another development, officials confirmed that Jerry Friedheim, onetime assistant secretary of defense for public affairs to California last week to talk with Reagan about the new administration's press operations. Friedheim, who is now an executive of the American Newspaper Publishers Association, is under consideration for White House press secretary himself, but officials said no decision on filling that job is expected until the future White House chief of staff, James A. Baker III, returns for vacation after the first of the year.

Reagan discussed his nearly completed Cabinet with reporters before and after a visit to an ear clinic in Los Angeles. The president-elect has acknowledged some loss of hearing in one ear, attributing it to an accident in his movie-making days.

He said the Cabinet meets one of his main goals in that "almost all of those people had to take a very definite step down from their own personal achievements and private lives in order to take government jobs." Perhaps reflecting on the big salary cuts for those coming from top-level industry, business and law firms, Reagan laughingly observed, "Some of them took more than one step down -- a great big step. They jumped off the bridge."

But he added that "it is a Cabinet of great quality, and I think it should inspire confidence in the people in almost every field as to what we are trying to do."

Aside from Haig, who told reporters he feels no "culpability" about his part in Vietnam or Watergate during his service in the Nixon White House, the most controversial selection has been that of Watt as interior secretary.

While Reagan was defending Watt yesterday as "a common sense man who is a reasonable environmentalist but who can also handle the problems of the Department of Interior," Watt himself was being asked what he considered an "environmental extremist."

The secretary-designate, who worked for seven years in the Interior Department, said he knew it was the site of "tremendous conflict" between developers and environmentalists. The "extremists," he said, "are those who would deny economic development and the balanced management of our resources for the benefit of consumers and all of America.

"We cannot afford to lock up, or utilize, our basic resources for one specific purpose. We must have the multiple use of those resources, as Congress has ordered. . . ."

A bit later, Watt identified himself with the "Sagebrush Rebellion," the western protest against federal public lands policy, but said that the demand for return of those lands, to state or private control could be eliminated by changing from an "oppressive landlord" to a "good neighbor" approach.

Except for Watt, all the selections introduced yesterday -- including secretary of labor-designate Raymond J. Donovan -- avoided substantive policy comments prior to their confirmation hearings.

Edwards was pressed by a South Carolina reporter to explain how his careers in dentistry and state government qualified him to run the Energy Department. The former governor said he had would on nuclear energy policy in the state legislature and in the National Governors Association, then drew a laugh by adding, "Some of my patients may have thought I drilled too deep. . . ."

There was a bit of surprise at Donovan's response to a question on his attitude toward Jackie Presser, a Teamsters official whose appointment to a transition advistory post was criticized by union elements who have accused him of underworld ties. After pointing out that he had played no part in the Presser appointment, Douovan said, "I look forward to meeting him."