The Reagan administration, accusing President Fidel Castro's communist government of lying to its people for 20 years, yesterday announced plans for a U.S.-sponsored radio station that will broadcast to Cuba in Spanish and "tell the truth to the Cuban people."

At a White House background briefing, senior administration officials said the station will be called Radio Marti in honor of Jose Marti, the father of Cuban independence, and will be similar in its operation to Radio Free Europe and Radio Liberty, which have broadcast respectively to communist Eastern Europe and the Soviet Union for more than 30 years.

The officials added that Congress will be asked to appropriate $10 million to fund the radio's operations and that current plans call for broadcasting to begin from a still-undetermined location in January.

The announcement marked a new turn in the exchanges of rhetorical hostility that have been going on between Washington and Havana since early this year when the administration accused Cuba of supplying arms to the leftist guerrillas in El Salvador and attempting to foment subversion throughout the Caribbean region.

The acrimony reached a new height last week when Castro, in a speech opening an international conference in Havana, attacked the Reagan administration as "fascist," "genocidal" and "covered in blood." The administration then recalled Wayne S. Smith, head of the U.S. interests section and the top-ranking U.S. diplomat in Cuba, for consultations.

In an announcement prior to yesterday's briefing, Reagan's national security affairs adviser, Richard V. Allen, charged that the Castro government has kept the Cuban people ignorant of its international subversive activities "through its control of the media."

"This administration has decided to break the Cuban government's control of information in Cuba," Allen said. "This radio service will tell the truth to the Cuban people about their government's domestic mismanagement and its promotion of subversion and international terrorism in this hemisphere and elsewhere.

"It will tell the Cuban people what these activities cost in terms of living standards for them and their children and will correct the false image they have been given of Cuba's international reputation," he added.

In describing the radio's aims and activities, the officials made clear that it will go beyond the kind of broadcasting engaged in by the Voice of America, which attempts, in a variety of languages, to provide straightforward international news and a picture of life in America.

Instead, the officials said, Radio Marti will be modeled on Radio Free Europe and Radio Liberty, whose broadcasts are intended as a substitute for information that cannot be found in the controlled press of the target countries. The officials said its content will include news about internal events in Cuba, commentary and possibly entertainment features.

Operation of the radio will be directed by a nonprofit corporation similar to that overseeing Radio Liberty and Radio Free Europe. Those two broadcasting activities were placed under that kind of control by Congress about 10 years ago after it became publicly known that most of their funding was supplied covertly by the Central Intelligence Agency.

The officials said that Congress will be asked for similar legislation to establish the proposed new radio, which will operate on AM frequency. They acknowledged that Cubans already can pick up many U.S. radio stations broadcasting from southern Florida, but said these broadcasts dealt mainly with U.S. affairs rather than conditions and events in Cuba.