"Cyrus? Cyrus who?" State Department officials quipped in embarrassed recognition of how the week's events in the Middle East had caught Secretary of State Cyrus R. Vance out to lunch during a dramatic moment of diplomatic history.

At a time when President Carter was proclaiming that "the eyes of the world are on Jerusalem," Vance was facing in another direction - taking off on a trip to Argentina, Brazil and Venezuela.

It didn't seem the most appropriate moment for the administration's top diplomat to be jetting around countries that aren't exactly on the front burners of U.S. foreign policy. Inevitably, it raised some pointed questions about the State Department's priorities and their relevance to the real world.

Department officials, while conceding that the timing was outwardly awkward, still insist the trip was a necessary, important item on the agenda of worldwide U.S. concerns and well worth a four-day detour from Vance's concentration on the Middle East.

Originally, Vance was supposed to visit Argentina in advance of Carter's now-aborted global tour and then join the President on the Venezuela and Brazil legs of his swing around the world.

After the Carter trip was put off, Vance's itinerary was expanded to include the other two countries - partly to soothe feelings ruffled by the President's cancellation and partly to attend to some important matters pending between Washington and the three South American governments.

Further tinkering with the schedule to allow Vance to remain in Washington during the Egyptian-Israeli summit would have seemed a breach of diplomatic etiquette, department sources say.

But, they quickly add, the trip was far more than an observance of diplomatic niceties. Vance, they note, isn't Secretary of State just for Middle East affairs; he has to keep a finger on U.S. relations with every area of the world.

Inevitably, the biggest share of his attention must go to crisis management in regions like the Middle East explosion. But the job also means trying to identify and solve problems in other areas that someday could become centers of tension and crisis.

In that context, the sources say, few regions have figured more prominently in the Carter administration's thinking than Latin America - for more than a decade a neglected step-child of U.S. foreign policy.

The President, they insist, is keenly interested Latin America. He has demonstrated that interest in a number of ways: by his assiduous efforts to master Spanish, by his dispatch of a constant stream of administration big names like Vance and Carter's wife, Rosalynn, to the area, and by rescusing those parts of the government that deal with Latin American policy from gheto status and giving them a bigger role in the formulation of diplomatic initiatives.

In fact, when administration officials are asked to name the foreign policy milestones of Carter's first year, they invariably turn to Latin America and cite the Panama Canal treaties and the move toward improved relations with Cuba.

Except for the continuing furor over Panama, most of this has gone unnoticed by the U.S. press and public. Within Latin America, though, it has stirred an excitement that has made Carter the most popular U.S. leader since President Kennedy and his Alliance for Progress of the early 1960s.

Indeed, among many Latins there is a tendency to equate Carter's interest in their region with a return to the policies that were disrupted by Kennedy's assassination and the Vietnam war.

It's a comparison that makes Carter administration officials decidedly uncomfortable. Despite surface similarities, they say, Carter's policies differ from those of the Kennedy era in many fundamental respects.

These differences include abandonment of the technocratic premise that Latin America's economic and social problems can be solved by massive amounts of U.S. financial aid.

Jettisoned, too, has been the old ideological tendency to view the region as an arena of Cold War rivalries, with Washington fighting to stem the encroachment of communism or other radical systems.

Most importantly, the administration has adopted the position that Latin America is too big and too diverse to fit inside what one official calls "the skin of a single policy, whether you call it the Alliance for Progress or whatever, that can be stretched to include all the political, economic and geographic differences of the region."

The new approach, he adds, was outlined by Carter April 14 when he told the Organization of American States: "A single United States policy toward Latin America makes little sense . . . Together we will develop policies more suited to each nation's variety and potential."

The result, State Department sources say, has been the still evolving development of a wide range of policies, each aimed at dealing with different Latin countries or areas in terms of their specific common interests or conflicts with the United States.

There is, for example, a Mexico policy, designed to take into account Mexico's position as a next-door neighbor and its role in the U.S. illegal immigration problem; a Brazil policy, predicated on the assumption that Brazil's size and resources make it a potential world power; a Venezuela policy, influenced by its role as a major supplier of crude oil to the United States, and a Caribbean policy, which recognizes that much of the region is culturally and geographically distinct from the rest of Latin America and aims at promoting greater cooperation among the Caribbean countries.

In dealing with Latin America on this country-to-country basis, the administration has taken special care to stress the promise made by Carter in his OAS speech: "I will be particularly concerned that we not seek to divide the nations of Latin America one from another or to set Latin America apart from the rest of the world."

Terence A. Todman, asistant secretary of state for Latin American affairs, explains: "If we give what looks like more emphasis to Brazil than some of the smaller countries, it's because we have to recognize the reality of Brazil's potential for playing a greater role in world affairs.But it doesn't mean that we're trying to set Brazil up as our surrogate leader of Latin America."

Similarly, Todman and others are mindful of the President's warning about not setting Latin America apart from the rest of the world." That, they say, means that the administration has abandoned the premise that Latin America, because it is a part of the Western Hemisphere, is an area that has special claims on the United States and where the United States has a special right to intervene when it sees fit.

Instead, the new approach is to consider Latin America as a part of the Third World - a region whose problems, aspirations and alliances are increasingly bound up with those of other underdeveloped countries in Africa, the Middle East and southern Asia.

That means dealing with Latin America within the larger context of the North-South dialogue. In taking this tack, the administration has quietly thrown overboard some of the most entrenched precepts of traditional U.S. policy.

One effect has been the application to Latin America of U.N. Ambassador Andrew Young's call for "divorcing the North-South dialogue from the East-West conflict." In marked contrast to the attitude in force from te promulgation of the Monroe Doctrine to Henry A. Kissinger's interference in Chile, the Carter people have acknowledged that the United States has no right to dictate what governments or political systems can hold power in Latin America.

Instead, the administration has said repeatedly, the nations of Latin America should be free to pursue capitalism, Marxism or any other system that they feel best suits their needs.

Viewing Latin America in the context of the Third World also has meant that many of the traditional problems in U.S.-Latin relations-human rights, trade questions such as tariff preferences and prices for raw materials, arms control and nuclear proliferation - are now being treated as part of U.S. global policy rather than as regional issues.

The way in which these different policy strands come together was illustrated by Vance's trip. In Argentina and Brazil, the two South American counties with a serious capability for developing nuclear power, much of the discussion involved the U.S. campaign to keep Latin America free of nuclear weapons.

Both countries also are military dictatorships that frequently have been charged with repression. Accordingly, Vance took the opportunity to remind his hosts of the Carter administration's commitment to human rights and urge them to ease the controls over their people's lives.

In Venezuela, Vance's main task was to reiterate U.S. opposition to new increases in the world price of crude oil and to urge that Venezuela, as an influential member of the Organization of Petroleum Exporting Countries, convey this view to other OPEC members.

Except for winning Argentina's agreement to ratify a treaty banning nuclear weapons, the trip failed to produce any major agreements on other trophies of diplomatic achievement. But, administration sources say none was expected.

Vance's trip, they add, was designed not for dramatic breakthroughs, but as one step in the slow, tedious process of re-establishing Latin American confidence in the United States after a decade of neglect,and putting U.S. Latin relations on a new footing of realism and mutual respect.

That there's still a long way to go is perhaps best illustrated by the problem of human rights - a concept brought to the forefront of world attention by the Carter administration and which has particular application to Latin America.

From Central America down through the Southern Cone region of Chile, Argentina and Uruguay, the prevalence of military dictatorships has made human right a major factor in U.S. dealing with latin governments. There is no other part of the world where Washington has put more effort into using foreign aid and other carrot-and-stick methods to produce improvements in the human rights climate.

So far, the effort has produced little in the way of dramatic successes. But it has provoked a lot of criticism, both from opponents who charge that the policy has only alienated traditional allies like Brazil and from human rights activists who argue that the administration has been too quick to reward dictators for the most minimal, cosmetic improvements.