The Reagan administration has told governments throughout the world that Cuba has made the Caribbean island nation of Grenada "a virtual client" and is plotting to control Nicaragua and overthrow the governments of El Salvador and Guatemala.

The U.S. assertions, contained in a lengthy confidential report on Cuban "covert activities" in Latin America, were dispatched to more than 50 American diplomatic posts early last month to be passed to political and governmental figures in the host countries.

The briefings for overseas leaders and governments are part of an administration drive, including public statements by its highest officials, to depict Cuba as an increasingly dangerous menace to international stability.

Secretary of State Alexander M. Haig Jr. will continue the drive this morning at a foreign ministers meeting of the Organization of American States at St. Lucia in the Caribbean. The State Department, while saying that Cuban activities are not on the formal agenda, has indicated that Haig plans to discuss the issue with Latin leaders in three days of bilateral conversations there.

Cuban President Fidel Castro, evidently reacting to the "covert activities" briefings and other similar efforts in recent months, has accused the United States of waging a "campaign of falsehoods and lies" to set the stage for actions "being prepared by the U.S. government against our country."

Haig and other senior administration officials have refused to rule out military or other action in Central America in response to Cuban activity and developments in Nicaragua, El Salvador, Guatemala and other nearby states. Discussions on the matter within top levels of the administration are reported to be at a sensitive stage.

The "covert activities" report, cabled from the State Department Nov. 8 to all U.S. diplomatic posts in the Americas and to 24 economically advanced nations throughout the world, charged that "since 1978 Cuba has markedly intensified covert efforts to stimulate armed violence and destabilize its neighbors, abandoning its earlier policy of fostering state-to-state relations."

The secret Cuban effort, according to the report, "does not discriminate between democratic governments and dictatorships" in the hemisphere. The report charged that "Democratic Colombia, Jamaica, Costa Rica and the Dominican Republic have all suffered Cuban interference in their internal affairs."

"Cuba's immediate goals are to exploit and control the revolution in Nicaragua and to induce the violent overthrow of the governments of El Salvador and Guatemala. At the same time, Cuba is working to sustain terrorism in other countries, and to fan political instability in the hemisphere," the document charged.

Most of the covert operations, according to the report, are planned and coordinated by the Americas department of the Cuban Communist Party. "Agents of the Americas department are present in every Cuban diplomatic mission in Latin America and the Caribbean--in at least five recent instances in the person of the ambassador or charge d'affaires," the report charged.

At least 22 Cubans attached to the Cuban Embassy in Mexico City and more than half of the Cuban government employes in Panama are intelligence agents, the U.S. document charged.

Among the specific allegations in the lengthy document are that:

* Cuban influence in Grenada "mushroomed" after the coup in March, 1979, that brought to power the current government, which "has slavishly followed a pro-Soviet foreign policy line."

Construction of a new Grenadan airport with "millions of dollars" from Cuba and Soviet equipment "will give Cuba a guaranteed, Cuban-controlled point for military flights to Africa," the U.S. document said.

* "Cuba presently is using Nicaraguan territory to provide training and other facilities to guerrillas active in neighboring countries."

The report alleged that 5,000 Cuban advisers of all sorts, including 1,500 to 2,000 military and security advisers, are working in Nicaragua, and that Cuba, the Soviet Union and Eastern European countries have supplied approximately $28 million worth of military equipment to Nicaragua, including tanks, light aircraft, helicopters, heavy artillery and surface-to-air missiles.

* Cuba "played a key role" in arranging the supply of weapons to Salvadoran guerrillas and has arranged contacts between the guerrillas and radical Arab states. In September, 1980, the report charged, Cuba "laundered" $500,000 in Iraqi funds for Salvadoran insurgents.

The State Department report on Cuban covert operations was presented to an Oct. 14-16 meeting in Brussels of Latin American experts of North Atlantic Treaty Organization countries before being cabled widely Nov. 8.

U.S. diplomats were instructed not to give the text of the report to the "appropriate political and governmental officials" who were to be presented with the gist of it. But the diplomats were asked to report "any significant reactions."