President Reagan began his Latin American trip yesterday with a declaration that he intends to promote "the cause of democracy and peace" and carried promises from congressional leaders for action on key portions of his Caribbean development plan.

In a three-minute statement on the White House South Lawn before departing for his week-long trip, the president said that congressional leaders had "agreed" to his request for quick approval of the trade and tax provisions of the Caribbean Basin Initiative, designed to encourage U.S. investment and trade in the region.

Arriving late last night in Brasilia, the capital of Brazil, Reagan struck a conciliatory note.

"We all know of the strong and steady advance of Brazil, both domestically and internationally," Reagan said in a brief airport statement. "Your elections Nov. 15 demonstrate Brazil's confidence in itself and its stability in freedom. Similarly, the management of the Brazilian economy through times of economic difficulty around the world inspires us all that our present problems can be overcome."

Reagan observed that the United States and Brazil have "areas of disagreement," a reference principally to U.S. objections to Brazil's subsidy of exports as well as its increased friendly ties with Cuba.

But Reagan, in a tone that is expected to predominate in his three days of meetings in Brazil, emphasized that "we also have a great deal in common" and said that he believed his talks with Brazilian President Joao Baptista Figueiredo will be fruitful and prove beneficial to both our countries."

In a statement by Reagan that was broadcast on Brazilian television last Friday, Reagan paid tribute to Figueiredo, who visited Washington last May, and said that the United States and Brazil were the economic leaders of their respective continents and would weather their current economic problems.

"The winds of economic crisis have buffeted our nations over the past few years--inflation, energy shortages, high interest rates--and we are still struggling to gain ground and prosper in these turbulent times," Reagan said. "Both Brazil and the United States have demonstrated during the same month of November that democracy is the world's best hope for peaceful change and progress."

It was a reference to mid-term elections that showed opposition gains in both countries, although both Reagan and Figueiredo apparently believe that their administrations remain in firm control.

In his statement on the White House lawn, Reagan made public written responses to questions submitted by Latin American newspapers, saying that he expected action on the trade and tax aspects of the Caribbean initiative before Christmas. In September, Congress approved $350 million for the emergency aid portion of the program.

Reagan said on departing on the four-nation tour that "we need more than just an injection of critically needed funds." He said he "underlined the importance" of action "as soon as possible" on the trade and tax aspects of the Caribbean initiative in a session with Republican congressional leaders earlier in the morning, "and they agreed."

The president said he talked also with Rep. Dan Rostenkowski, (D-Ill.), chairman of the House Ways and Means Committee, who recently traveled to the Caribbean at the request of the administration. Reagan said Rostenkowski also "promised to help" pass the Caribbean development plan in the lame-duck session. A spokesman for Rostenkowski said, however, that his commitment to help Reagan in the lame-duck session included the trade aspects of the Caribbean Basin Initiative but not the tax aspects.

The president said his "working visit" includes talks with six presidents and will focus on steps to revive flagging domestic economies, "to reduce the threats to peace and security," and to promote the "continued development of democracy."

"The four countries I am visiting have all had elections in the last year," Reagan said. "There is a strong democratic tide running in the Americas."

From Brazil, the president will travel to Colombia, Costa Rica and Honduras.

In his written responses to the Latin American newspapers, Reagan cited the situation in El Salvador as "a good example of the tension and instability" that can flow from international economic troubles.