President Reagan and Brazilian President Joao Figueiredo yesterday sought to improve the sometimes rocky relationship between their countries despite new complications arising from the Falklands conflict.

The British-Argentine conflict, which has positioned the United States on the opposite side from Brazil and most other Latin American countries, was treated gingerly in the public comments of the two leaders. U.S. officials said, however, it was the principal focus of their private talk.

Figueiredo, who referred to the conflict in the White House welcoming ceremony only as "the present difficult circumstances," cut short his visit here by one day because of it, evidently to avoid being seen as too close to the United States.

In the meeting with Reagan, according to a White House briefing, the Brazilian expressed hope for an early settlement of the Falklands dispute "with neither victors nor defeated, but with the honorable and just requirements on both sides having been met."

Reagan, who did not allude to the Falklands in his public welcome, agreed with the Brazilian's hopes for settlement, especially in the context of current efforts by U.N. Secretary General Javier Perez de Cuellar, the U.S. briefer said.

Brazil, the largest and in many respects the most important country of South America, has recently improved its relations with its traditional rival, Argentina.

Brazil, a moving force behind the pro-Argentina resolution adopted by the Organization of American States late last month, has supplied military equipment to Argentina, including three reconnaissance aircraft, since the conflict with Britain erupted.

U.S. officials said that to their knowledge Brazil's arms sales to Argentina were not discussed in yesterday's talks.

Also not discussed by the two leaders, the officials said, was the situation in Central America, where Washington has placed its greatest hemispheric priority.

The topic was taken up with the Brazilian later by Secretary of State Alexander M. Haig Jr., U.S. sources said, adding that the exchange of views did not include a U.S. request for Brazilian involvement.

Figueiredo's brief address at the White House welcoming ceremony, while expressing friendship, was reserved in tone. He spoke of his country's "diversified" foreign policy and its "balanced relations" with the United States.

U.S.-Brazilian relations have improved substantially since a low point during the 1970s, according to Washington specialists, but the remaining scars and the new problem of the Falklands dispute stand in the way of a warmer embrace.

Brazil's large-scale economic problems as a major oil-consuming country with a big international debt may have been compounded by U.S. high interest rates and some recent Washington developments.

Among the items raised by Figueiredo with Reagan was the recently imposed U.S. quota on imported sugar, which is expected to cut Brazil's shipments of sugar to the U.S. market by at least half and possibly two-thirds at a time when Brazil has a bumper sugar crop and needs the money it could bring.

Reagan, according to the White House briefing, put the blame on Congress, saying that the lawmakers, not the administration, had "imposed" the sugar price-support program, which required establishment of the import quotas.

The president did not oppose the sugar price-support legislation, reportedly in exchange for several southern votes for his budget proposals last year.

Figueiredo also raised U.S. efforts to disqualify Brazil from receiving subsidized loans from the World Bank on grounds that the South American giant, with a per capita income of more than $2,300 yearly, is no longer one of the world's neediest cases.

Reagan responded that "a pragmatic compromise" on this issue should be arranged.

The Brazilian president is due to leave Washington this evening for a checkup at the Cleveland Clinic, where he was treated for a heart attack last fall.