MOSCOW -- In the strongest indication yet of rising Soviet interest in forging broader and closer relations with Latin America, Soviet Foreign Minister Eduard Shevardnadze began a week-long trip through the region yesterday.

The trip -- which includes stops in Brazil, Argentina and Uruguay -- is the first that a Soviet foreign minister has ever made south of Mexico.

The venture marks the high point of a year-long Soviet diplomatic effort to develop closer contacts with the relatively new democracies in South America while widening ties in Central America beyond Cuba and Nicaragua, the two prominent Marxist-ruled countries in the region. The Soviet minister will also stop in Cuba.

Shevardnadze's visit, which began yesterday in Brazil, is also widely regarded as foreshadowing an expected trip by Communist Party leader Mikhail Gorbachev, possibly next year.

The Soviet foray into Latin America, part of an overall effort at broadening relations beyond communist eastern Europe and into other areas of economic and strategic significance, is viewed by western diplomats in this Soviet capital as among the most sensitive and risky of the new diplomatic ventures attempted by Shevardnadze and Gorbachev.

The diplomats point out three potential dangers for the Soviet Union in the area:Being viewed as a potential source of economic aid at a time in which Moscow, faced with its own economic problems, is seeking to rationalize and trim aid across the board to the Third World.Clashing with Washington over U.S. policy in the region, particularly in Central America, which remains a top priority interest of the Reagan administration.Creating an antisocialist backlash in the region, which is peppered with conservative governments as well as many newly liberal governments that in recent years have succeeded military regimes.

And yet, the interest in closer Soviet-Latin America ties seems to be mutual. This year, governmental or parliamentary delegations from at least a dozen countries in Central or South America have visited Moscow. President Raul Alfonsin became the first Argentine head of state to visit Moscow in October of last year.

Among the results of the visits were the first Soviet cultural agreement with Guatemala and its first trade agreement with Honduras.

The trips to Moscow climaxed last week when representatives from 14 Latin American countries wrapped up an eight-day seminar on economic integration in the region.

"Latin America," Soviet Foreign Ministry spokesman Gennadi Gerasimov said in a recent briefing, "is beginning to discover the Soviet Union."

Apparently aware of the risks involved in the relations, however, both the Soviet Union and its Latin interlocuters seem to be exercising caution. Diplomats said, for example, that last week's Moscow seminar, appeared to focus on general economic problems and avoided party line speeches. Similarly, Shevardnadze first signaled stronger Soviet interest in the area with a low-key trip to Mexico.

During political tension between Washington and Panama last spring, a parliamentary delegation from Panama visited the Soviet Union but a diplomatic source said the trip produced little because both sides thought it best to go slowly in developing relations.

There are also some signs that Moscow is being more careful in its dealings with politically volatile Nicaragua, its main client in the region aside from Cuba, in an apparent attempt to keep in line with the more skeptical and demanding policy toward the leftist Sandinista government now formally emerging from other Central American countries.

The Soviet Union earlier this month rushed out an endorsement of the five-nation Central American peace plan signed in Guatemala Aug. 7, while Washington appeared critical of it. The plan would force the United States to halt aid to forces trying to unseat the Soviet-Cuban-backed government in Managua, but also calls for the Nicaraguan government to open its political system to the opposition.

Earlier this year, Moscow indicated it would not increase its supplies of oil to Nicaragua, despite the fact that supplies from other Soviet Bloc countries would be cut back. The Soviets reportedly have relented somewhat since then.

Latin American and western diplomats in Moscow interpret the Soviet policy of avoiding too heavy-handed support for Nicaragua as part of an attempt to keep from further ruffling relations with the Reagan administration and at the same time to keep open the option of closer ties with several other countries, such as Honduras and Brazil, which are likely to be leery of blatant Kremlin dealings with Managua. The approach is consistent with an overall policy Gorbachev has stressed of steering clear of new commitments to revolutionary movements.

Soviet Latin America-watchers say one of Moscow's major interests in the region is economic. Latin America, rich in resources, could become a strong trade partner.

For now, however, Soviet-Latin American economic relations are at a low level. Soviet trade with Brazil plummeted from $833 million in 1983 to $310 million last year, for example. Even trade with Argentina, a longtime supplier of wheat, has suffered in the last two years.

The situation bears out what some Latin American diplomats in Moscow consider to be the biggest barrier to Soviet influence in the region: financial woes.

"What we really need is aid," one Latin American diplomat said, "or at least a viable market for some of our goods. At the moment, Moscow cannot offer much of either."

For Latin American nations the Soviet overtures offer a way to move away from what some see as excessive and longstanding U.S. influence in the region.

"The democratic countries of Latin America are greatly intrigued by glasnost," said Cole Blasier, professor of political science at the University of Pittsburgh, referring to Gorbachev's policy of "openness."

"The Brezhnev regime was no alternative to the U.S.," he added. "Gorbachev is appealing because he provides an alternative, a counterbalance to the influence of the United States."

"The most important countries, of course, are Argentina and, especially, Brazil," says Jiri Valenta, director of Miami University's Institute of Soviet and East European Studies. "The Soviets believe in Nixon's remark that the way of Brazil will be the way of the continent."

"In the past, the Soviet Union saw the Latin American countries as part of the U.S. empire," Valenta said. "Soviet policy is to encourage a drift toward independence away from the United States." David Remnick of The Washington Post Foreign Service contributed to this article in Washington.