The Cuban government yesterday made its most public and dramatic move in this country since Fidel Castro took power to mend relations with the Cuban-exile community in the United States, most of which has been ferociously hostile to Castro.

In his first press conference, Ramon Sanchez Parodi, chief spokesman here for Catro, invited leaders of the Cuban community in the United States to go to Havana and help work out programs for release of political prisoners, reunification of severed families and visits to Cuba by expatriates.

Sanchez Parodi said there is considerably less hostility than previously to the government of Cuba among Cubans living in the United States.

Therefore, " now is the moment " to open discussions " as early as possible, " he said.

Sanchez Parodi heads a 10-member diplomatic group called the " Cuban Interests Section, " which the United States allowed to be stationed here last September. It represents the Castro government and is located at the Czechoslovakian embassy.

The idea of a "dialogue" between Castro and Cubans living in other countries was enunciated by Castro Sept. 6 in a meeting with foreign reporters.

Sanchez Parodi said he had called the press conference to reaffirm and restate as clearly as possible that the Cuban government wants to set up broad programs for possible release of most of 3,000 political prisoners, reunification of families and visits to Cuba.

Several sources said Sanche Parodi's first press conference here appeared to be an attempt to emphasize in the most dramatic way that Cuba wants to decrease tension and hostility with the community of overseas Cubans. Sources also said that Sanchez Parodi's statement appeared to be an attempt to convince the United States that Cuba is serious about improving relations with the U.S. government as well as with the exiles. It is the first time the Cuban Interest Section has taken an active public role in broadcasting Cuban government policy.

He said the Cuban government recognizes that attitudes toward it among Cubans living abroad vary widely and there is no single spokesman or representative group. Cuba isn't expecting the U.S. Cuban community to hold a referendum or election to choose representatives, but wants to sit down with a variety of leaders - other than those representing "terroist activities" - to develop a systematic approach to the three problems, he said.

He said the discussions should be viewed as involving only the Cuban government and Cuban-origin people living abroad. They would be "parallel to" but not directly linked to any government-to-government discussions with the United States on improvement of relations and settlement of problems between the governments.

Sanchez Parodi said many groups of Cubans living in the United states no longer have the same "hostile" attitude toward Castro, and some contacts have been made with some of these groups.

He said some prisoners have been released, some families reunited and some visits allowed, but on a case-by-case basis. If "we could find [systematic] ways to address these problems, we will not be forced to address them on a case-to-case basis," he said.

Asked whether the discussions would include possible release of a half dozen Americans being held as political prisoners as well as the 3,000 Cubans in that category, he said "that's another issue" to be handled by other methods.

Cuba has submitted to the Justice Department the names of 334 political prisoners it is willing to release for emigration to the United States. The first 46 names were processed and the group arrived in Miami Oct. 21, accompained by more than two dozen relatives.

The State Department said after the 46 prisoners arrived last month that their release "obviously improved the climate" of relations but many problems are still outstanding, including the Cuban presence in Africa.