President Carter laid down a set of conditions yesterday for moving toward normal relations with Cuba that go far beyond both his previous positions, and the publicly expressed views of Secretary of State Cyrus R. Vance.

The President gave his views in a brief but sweeping off-the-cuff reply during a question-and-answer session with Agriculture Department employees.

"I would like very much to see the Cubans remove their soldiers from Angola and let the Angolan natives make their own decisions about their government," he said.

"We've received information from indirect sources that Castro and Cuba have promised to remove those troops. And that would be a step toward full normalization of relationships with Angola.

"The same thing applies ultimately to the restoration of normal relationships with Cuba.

"If I can be convinced that Cuba wants to remove their aggravating influence from other countries in this hemisphere, will not participate in violence in nations across the oceans, will recommit the former relationship that existed in Cuba toward human rights, then I would be willing to move toward normalizing relationships with Cuba as well."

The statement took Carter far beyond his position in October, when he told a Kansas City news conference:

"I don't see any immediate prospect for the normalization of relationships with Cuba. And I don't advocate that as a goal for our country in the foreseeable future . . ."

Last Sunday, during his roving, three-hour news conference in Plains, Ga., he said the key element in relations between the United States and Cuba was the issue of human rights. He said he hoped a recent statement by Prime Minister Fidel Castro indicating a desire for improved relations "can be followed up by mutual efforts to alleviate tensions and reduce animosities."

Vance, during an initial meeting with the reporters Jan. 31, was asked whether his position on Cuba was similar to that of former Secretary of State Henry A. Kissinger, who stressed the removal of the 13,000 or more Cuban troops in Angola as a condition for normalizing relations.

"I don't want to set any preconditions at this point . . .," Vance said. He has made no differing public statement since that time.

Neither the White House, nor the State Department, was prepared to add any details to Carter's statement, which appeared to catch them by surprise.

Left unexplained were the identity of the "indirect sources," what evidence Carter would accept from Cuba as an indication of its intentions, and the role of Mexican President Jose Lopez Portillo, who said Tuesday after two days of talks with Carter that he saw "goodwill on the part of both nations to solve this situation."

Reports from Havana in early February indicated that Cuban leaders may have been surprised by the speed with which the Carter administration has signaled a possible thaw in relations.

Rep. Jonathan B. Bingham (D-N.Y.) who visited Cuba last week and talked with Castro, said yesterday the Cubans told him at least half of their troops in Angola had been withdrawn, and that "thousands of technicians, doctors and teachers" had been sent instead.

From Cuba's viewpoint, Bingham said the first step toward normal relations must be a lifting of the U.S. trade embargo, imposed a year after the United States servered diplomatic relations with Cuba in January, 1961.

Carter's question-and-answer session with Agriculture Department employees, and a similar session an hour earlier at the Department of Health, Education and Welfare, were part of a series of carefully planned, high-visibility events that have marked his presidency.

He used both appearances yesterday in the same way he did four he made last week at other government Cabinet level departments - to deliver a low-keyed blend of pep talk and fatherly advice without the traditional ceremony surrounding a presidential visit.

Carter also:

Told cheering HEW employees, There will never be any attempt while I'm President, to weaken the great civil rights acts that have passed in years gone by."

Said that by the end of this year, he intends to have a timetable for a year-by-year phasing in of comprehensive national health care.

Said he will nominate Douglas M. Costle as administrator, and Barbara Blum as deputy administrator, of the Environmental Protection Agency. Costle is now assistant director of the Congressional Budget Office.

The President's decision not to appoint Blum, his deputy campaign director and operations director of his transition team, to head an agency angered feminists when it was announced in late January.

Disclosed that he has asked all Cabinet officers to tell him by March 31 how they will reduce by 8 per cent the 143.1 million work hours Americans are required to spend filling out reports to federal agencies.

Said he will nominate Georgia state budget director James T. McIntyre of Management and Budget. Carter appointed McIntyre to his present job. The head of OMB, Atlanta banker Bert Lance, is also a Georgian.

Carter said he also wants to change Social Security regulations and welfare payments that encourage family break-ups through absentee fathers.

Last week Carter told Labor Department employees that if they are "living in sin" they should get married, because the family is the foundation of wamerican Life.