Cuba's 14-member diplomatic mission here, which has been President Fidel Castro's most important channel of communication with the United States, is being cut loose by Czechoslovakia, whose embassy in Washington has sponsored the Cuban mission since 1977.

Although the United States and Cuba do not have full diplomatic relations, the "interests section" operating under Czechoslovak auspices has given Castro's hard-line communist regime the equivalent of a Washington embassy. Under a 1977 agreement, the United States has a similar interests section attached to the Swiss Embassy in Havana.

But two weeks ago, the new, democratically elected president of Czechoslovakia, Vaclav Havel, responded to pressure from U.S. congressional and human rights groups by informing the Cubans that they will have to find a new sponsor by the end of March.

U.S. officials said yesterday that Cuban failure to do so would require a shutdown of the interests section lodged in the old Cuban Embassy on 16th Street NW. Cuban Foreign Minister Isidoro Malmierca has said he is looking for another embassy to provide cover for the Cuban diplomats in Washington. Cuban officials said yesterday the search still is being conducted by the foreign ministry and that they have no information about which countries might be involved.

"The Cubans have not said one word to us about what they're planning, and we honestly don't know what countries they may have approached to put an umbrella over the interests section," said one State Department official familiar with Cuban affairs.

"The U.S. position is that we find the presence of the Cuban mission useful as a conduit for exchanging messages and transacting necessary business," the official added. "But it also is our position that it's their problem to solve. They haven't asked us for help, and we haven't offered any."

U.S. officials have said that relations with Cuba cannot be normalized until Havana ends its support of communist subversion in other countries and becomes more democratic. In particular, the United States insists that Cuba free thousands of political prisoners opposed to Castro's regime, halt its aid to leftist guerrilla movements in such countries as El Salvador and settle an estimated $2 billion to $3 billion in U.S. claims for property confiscated by the Castro government.

There has been speculation in diplomatic circles that Cuba might turn to Iraq, since Havana voted against the U.N. Security Council resolution authorizing force to end Iraq's occupation of Kuwait, or to Yemen, a radical Arab state that also has supported Iraq in much of the Security Council debate over the Persian Gulf crisis.

However, U.S. officials, noting that Iraq may be on the verge of war with the United States, expressed doubt that the Baghdad government or countries sympathetic to it would want to take on what one called "the added baggage of sponsoring Cuba's diplomatic presence here at this particular time."

The officials said that the reverses being suffered by communism in Eastern Europe and elsewhere might make it very difficult for Castro to find a "fraternal socialist state" to act as sponsor. But, the officials added, there probably are several neutral countries willing to take on a job that really involves nothing more than allowing the use of its name as an official cover for the interest section's largely independent operations.

Asked whether failure to find a new sponsor might cause Cuba to threaten closure of the U.S. interests section in Havana, a U.S. official replied: "That's up to them, but we frankly don't think it will come to that."