Cuban diplomats have begun pressing through private channels for full-scale negotiations between the United States and Cuba to defuse what they are calling a "very dangerous situation" that could lead to a "military confrontation in Central America" between the two nations.

The Reagan administration's response to this latest thrust in the verbal war games that have come to dominate the troubled Caribbean is a quick no.

"This administration is not about to talk to the Cubans about what is going on down there" while Cuba is sending military aid to guerrillas in El Salvador and elsewhere, said a State Department official.

This Cuban bid is taking place in the wake of one genuinely new development: a secret meeting in Mexico City a couple of weeks ago between Secretary of State Alexander M. Haig Jr. and Cuban Vice President Carlos Rafael Rodriguez, believed to be the highest-level talks since Cuba and the United States broke relations in 1961.

The Washington Post has confirmed a report, first carried in a Mexico City newspaper but never officially acknowledged by either country, that Haig and Rodriguez did meet in that city on Nov. 23. The session was characterized by an informed source as a wide-ranging discussion. But the source emphasized that it was not a prelude to negotiations between the United States and Cuba, and that no further meetings are planned between high-level officials of the two countries.

Just what took place at the meeting is not certain, nor in fact is it clear why the meeting was held at all, given Haig's frequent and recent hard-line warnings about Cuban military aid to rebel forces. Mexico has been anxious to serve as an intermediary between the United States and Cuba, however, and the United States has also been anxious to convince the Mexicans that Washington is sincere in its desires to improve its relations in the Americas in general and with Mexico in particular.

In recent days, Cuban diplomats attached to the Cuban Interest Section in Washington have begun contacting journalists to spread the word that Cuba is now seeking broad negotiations with the United States. At various times in the past Havana has sought similar broad bilateral negotiations with Washington, but for the most part, this year, they had not pressed the matter--until they began privately preaching the gospel of negotiation anew in the last few days.

"Cuba fears that the United States and Cuba are facing the possibility of a military confrontation in Central America," one Cuban envoy told a Washington Post reporter in a meeting arranged at the Cuban's request.

"We believe that this is a very dangerous situation. It is important now, more than ever before, to have negotiations between the United States and Cuba. Negotiations between the United States and Cuba are not only desirable but necessary at this point."

He said that such negotiations should cover the entire range of "bilateral" issues between the two countries. "The negotiations should be based on a mutual respect, taking into consideration Cuba's sovereign rights," he said.

Asked if the presence of Cuban troops in Angola and Ethiopia and elsewhere, and the extent of Cuban military aid within the Americas would be a subject for negotiations, he said: "I don't know if Cuban troops around the world would be a subject for negotiations. But there is also the question of United States troops in Europe and Asia."

Cuban officials have come to the view that negotiations are vital now, according to this envoy, because they are concerned about the tone and content of the recent hard-line comments of Haig and others about Cuban military aid around the world, especially in the western hemisphere. So far this year, U.S. officials have said, Cuba has received approximately 63,000 tons of Soviet arms, more than has been received in any year since the 1962 Cuban misssile crisis.

Haig warned during last week's meeting of the Organization of American States in St. Lucia that "the principle of nonintervention is being violated today" by Cuba.

These Reagan administration statements, counters the Cuban envoy, are based on a "misunderstanding and a misapprehension of the United States government." He went on: "It is not a secret to anybody that we have troops in Angola and Ethiopia, and military advisers in other countries . . . in Africa." But he added, "There are allegations that are false that Cuba is supplying weapons to the rebels in El Salvador and Guatemala. It is not true that we have passed Soviet weapons through Cuba to Nicaragua."

A State Department official, in rejecting the Cuban call for U.S.-Cuban negotiations, said:

"This administration is not about to talk to the Cubans about what is going on down there. I don't think this administration believes it should discuss this with the Cubans at all. . . . What are we going to do, negotiate with the Cubans so they will stop aiding the Salvadoran guerrillas?"

The State Department official noted that President Carter tried to initiate talks with the Cubans in 1977, after the two countries opened their respective "interest section" offices in Washington and Havana. But the Cubans followed up by sending more troops into Africa, he said, and the efforts to talk with the Cubans were suspended in December, 1977.