Rosalynn Carter said today that although the United States is "making gestures" to Cuba, "difficult problems" remain before normal relations can be resumed.

She mentioned American prisoners in Cuba and Cuban families who became separated, some living in the United States and some in Cuba, after the United States broke of diplomatic relations in 1961. She did not mention the question of compensation for American property expropriated by the government of Fidel Castro.

Mrs. Carter, on a two-week mission to seven Latin American countries, made the comments at a news conference in Kingston, Jamaica, before flying to San Jose.

She was greeted here by Marjorie Eliot De Obuder, wife of Costa Rican President Daniel Oduber, and by Foreign Minister Gonzalo Facio.

About 1,500 people, some of them lining two balconies of the airport building, waved American and Costa Rican flags and greeted Mrs. Carter enthusiastically.

The group cheered loudly when she said in Spanish that she was glad to be "in your beautiful country" and had "marvelous impressions of Costa Rica" from a trip she and her husband made here in 1972.

Earlier, at her Kinston news conference, Mrs. Carter noted that the United States and Cuba have opened travel opportunities and signed an agreement on fishing rights. She also noted that the United States has proposed that the two nations open "interest sections" in the embassies of third countries in Havana and Washington. This step is often a prelude to formal diplomatic relations."

"We have lots of problems" with the Cubans, she said, "but we are in a dialogue with them."

Mrs. Carter said she thought the problems could be worked out, but then backed off that assessment, saying: "I don't know if they can be worked out or not. They are very difficult problems."

She said that she'd has seven hours of discussions with Jamaican Prime Minister Michael Manley and that while he did not ask for U.S. aid, he did appeal for U.S. help in relaxing the requirements of international banks so Jamaica could receive loans more easily.

Asked what authority she had to speak for President Carter in discussions with foreign leaders, Mrs. Carter seemed to bristle and said firmly: "I think that I am the person closest to the President of the United States, and if I can help him to understand the countries of the world, that's what I want to do."

She announced that Carter will sign the American Convention on Human Rights, which was negotiated here in 1969, on Wednesday. Costa Rica and Colombia are the only nations that have signed it. Eleven countries must ratify it before it goes into effect.

President Carter said April 14 that he would sign it and ask the Senate to ratify it. The convention has several provisions that may cause controversy in Congress, including establishment of an inter-American court of human rights, compensation for victims of injustice and an article entitled the "right to life" dealing mainly with capital punishment.

Mrs. Carter's day began with a tour of a community center in the heart of Kinston. Called the Central Kinston Upgrading Project, the center provides day care, pre-school, library and counselling services at about 7,000 people in a five-block area. At least 30 per cent of them are unemployed.

The First Lady asked the name of a little girl, who told her it was Rosie.

"That's grea.t. Did you know that's my name, too?" Mrs. Carter asked.

She was mobbed by children as she walked down the street past houses with boarded windows, large holes in the stucco and rusted tin roofs. Turning a corner and walking down Tower Street, she met a schoolgirl in a white blouse and blue skirt, who ran to the First Lady and hugged her legs. The child, Paulette Aron, Stayed glued to Mrs. Carter for the rest of the tour.

They entered a day-care center made of reclaimed junk, including two salvaged buses used as classrooms. On one of the buses was a sign that said: "Life is serious and we must be careful. One misstep can cause you years of regret and grief and sorrow - without relief.

Mrs. Carter said she found it "really interesting to see how the government is upgrading a community."

Hundreds of people lined the streets and followed her as she toured the area. One Jamaican, a 26-year-old unemployed carpenter named Kenneth Smith, said he was hopeful about her visit.

"She can get more money for us so there will be more jobs," he said.