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Partial transcript follows:

The Cuban government is urging U.S. officials to sit down and talk about the fate of the jailed American Alan Gross who tells me he feels as though he's being held hostage in Cuba. Stand by for my exclusive, very rare interview with a top Cuban foreign ministry official in Havana. She spoke with me from Havana, but first, some background.

(BEGIN VIDEOTAPE)

BLITZER (voice-over): An international negotiation is seemingly playing out on CNN. It started Friday when Alan Gross, an American imprisoned in Cuba for the last two and a half years called into the SITUATION ROOM.

ALAN GROSS, IMPRISONED IN CUBA: I'm in Carlos Finlay Military Hospital. It's a secured facility.

BLITZER: During my 25-minute interview with Gross, we touched on several topics, including his health.

GROSS: I lost about 100 pound, and I exercise as much as I can. My hip is starting to give me a little bit of a problem.

BLITZER: The Maryland contractor who's now serving a 15-year prison sentence says he was in Cuba in the lengthy island's tiny Jewish community to the internet as part of the U.S.-funded aid program. The Cuban government disagreed, charging Gross with smuggling an illegal equipment and being a threat to the security and independence of the state.

GROSS: It was laughable, and if I weren't in this situation, I would be laughing about it, because I'm about as much of a threat to the security in the state as the chair that I'm sitting on right now.

BLITZER: Gross is now pleading with the Castro regime to let him fly to the United States and see his cancer-stricken 90-year-old mother. The government hasn't officially responded to his request. Instead --

GROSS: They offered to send a plane to Miami to bring her here. My mother does not live in Miami. My mother lives in Texas. She's not allowed to travel. That's baloney. I -- I'm trying to catch myself so I don't use a stronger word.

BLITZER: Shortly after that interview, the Cuban representative in Washington, Jorge Bolaños, sent CNN a letter refuting some of Gross' claims saying, quote, "Gross is in good, physical conditions. He receives specialized medical care, balanced meals, regular consular access, visits by friends, and political and religious personalities."

He added, "Mr. Gross violated Cuban laws by implementing a U.S. government program aimed at attempting against Cuba's constitutional order. He is not an activist who came to Cuba to assist the Cuban people. He is a professional paid for by the U.S. government."

Secretary of state, Hillary Clinton, fired back in an interview with CNN.

HILLARY CLINTON, SECRETARY OF STATE: Mr. Gross was not a spy. Mr. Gross was not an intelligence agent. Mr. Gross worked for a development group that was helping Cubans, principally, in their small Jewish community in Cuba to have access to the internet. and Mr. Gross, in our view, is being held without justification and has been detained already far too long.

(END VIDEOTAPE)

BLITZER: The letter I received from the top Cuban diplomat here in Washington, Jorge Bolaños clearly suggested to me that the Castro government is interested in a prisoner swap exchanging Alan Gross for members of the so-called "Cuban five". They're serving lengthy prison sentences in the United States after being convicted on spy charges. I've been reaching out to both Cuban and U.S. officials to try to clarify their positions and to also try to keep the lines of communication open.

(BEGIN VIDEOTAPE)

And Josefina Vidal is joining us now from Havana. She's the head of North American Affairs for the Cuban Foreign Ministry. Are you prepared to tell us what you want in exchange for the release of Alan Gross?

JOSEFINA VIDAL, CUBAN FOREIGN MINISTRY OFFICIAL: Wolf, thank you for having me in your program. We have conveyed to the U.S. government our willingness to have a dialogue to try to solve all our problems and to normalize relations between our two countries. In this specific case we have made clear to the U.S. government as you said that we are ready to have a negotiation in order to try to find a solution, a humanitarian solution to Mr. Gross' case on a reciprocal basis.

I am not -- we are not advancing any specific formula. It has to be discussed with the U.S. government because the U.S. government has a direct responsibility on the situation for the situation of Mr. Alan Gross, but again, we have been waiting for a response on the side of the U.S. government on this specific matter.

BLITZER: So there are no active discussions or negotiations underway right now between the Cuban government and the U.S. government to try to free Alan Gross?

VIDAL: We have conveyed to the U.S. side that we are ready to sit down to talk and to have a negotiation on this matter, and as I mentioned already to you, we have been waiting for a response. We are ready to do that.

BLITZER: Is there, from your perspective, is there a linkage between the release of Alan Gross and the release of what's called the "Cuban Five"?

VIDAL: Again, we are not advancing a specific solution, a specific formula. It has to be discussed among us, but definitely Cuba has legitimate concerns, humanitarian concerns related to the situation of the "Cuban Five".

BLITZER: What do you say in response to what the Secretary of State Hillary Clinton told CNN?

VIDAL: You know Mr. Gross was not working in Cuba as a volunteer, aid worker. He was detained in Cuba because of conducting a well-financed program by the U.S. government aimed at provoking changes in Cuba, attempting against Cuba's constitutional order. So Mr. Gross when he was retained was a professional under a contract by the U.S. government fulfilling this, trying to implement this program financed by the -- by some U.S. agencies.

BLITZER: What --

VIDAL: But he was -- he was, of course, in violation --

BLITZER: What evidence do you have that he was doing that?

VIDAL: He was convicted for violating Cuban laws, attempting against Cuba's constitutional order is not just a crime in Cuba. It is also a crime in the United States and in many other countries and this is the reason why he was convicted because of attempting against our independence, our constitutional order.

BLITZER: Mr. Gross told me that when he brought all of the equipment in the people at the airport, the authorities saw the equipment and they said you have to pay duty on it, 100 percent. He didn't want to pay 100 percent so they just said pay $100 and you can bring the equipment in, but they inspected all of those cell phones and all of the satellite phones, whatever he was bringing in and allowed him to bring it into the country. As a result, he says he doesn't understand why he was arrested.

VIDAL: It has been written in some media reports Mr. Gross misled U.S.-Cuban authorities about the kind of equipment he was introducing into the country without the proper authorities and he also misled members of the Cuban- Jewish community about the purposes of his trip to Cuba and what he was doing in Cuba.

BLITZER: Alan Gross says his 90-year-old mother is dying from cancer in Texas right now. She can't travel. She can't get on an airplane. He would like to spend two weeks and he promises he would come back to Cuba if you let him say good-bye, in effect to his mother. What's wrong with that?

VIDAL: In the case of Mr. Alan Gross he has started to serve his prison terms three years ago, and the conditions under which he is now do not allow him to go outside of Cuba.

BLITZER: Even for humanitarian reasons to visit his 90-year-old mother who has cancer and is dying? Are you open at all to letting him say good-bye to her?

VIDAL: In the case of Mr. Gross, we have guaranteed for him a good treatment as he himself told you. He's in good shape. He receives specialized medical treatment, balanced meals. He receives visits, regular consular access and visits by friends, by religious and political leaders from the U.S. and other countries and we have facilitated for their families and friends all the visits they have requested so far.

BLITZER: What do you think of President Obama and his efforts over these past three and a half years to reach out to try to improve relations between the United States and Cuba?

VIDAL: This is our position, I mean, for many years the Cuban government has been conveying to the U.S. side our willingness to have a comprehensive, political dialogue with the United States to solve all our historical problems and to move on in order to have a productive, beneficial relationship for the benefit of our both people, and this is our position. We have related that to the U.S. government and we are continuing -- are willing to have the possibility to see that future for our two countries.

BLITZER: Is there any dialogue under way right now between your government and the Obama administration?

VIDAL: We have had talks in the last two or three years. As soon as the new president, President Obama took office, some level of official dialogue that suffered a lot during the previous administration that was established and we have had our biannual migration talks and we have talked -- we have conveyed in those meetings the position I just described to you about Cuba's willingness to -- for the best of our two countries, to find a civilized -- civilized (INAUDIBLE) with the United States.

BLITZER: Are you hopeful? Are you optimistic that the relationship will improve over these next few months?

VIDAL: We are always hopeful. We have been waiting for that moment for more than 50 years, but we are still strong believers that the future is possible for the good and the benefit of the U.S., of Cuba, of our both mutual national interests and for our people.

BLITZER: Based on my conversations with very high U.S. officials, Ms. Vidal, I can tell you that if you were to make a gesture and release Alan Gross, he served already two and a half years that would go a long way in setting the stage for an improved U.S.- Cuban relationship.

VIDAL: In that regard I have to be honest with you, Wolf, and tell you that we see this statement as a new pretext by the U.S. side in order to -- not to move on, on our bilateral relationships. We have seen all over our history that any time one pretext disappears, there is another one ready at hand in order to try to justify not to normalize the relations with Cuba.

BLITZER: It sounds like a relatively easy situation for you, test the United States, send Alan Gross home and see what happens. If there's no improvement, what have you lost?

VIDAL: As I mentioned to you in the beginning of our interview, this is something that Cuba cannot do unilaterally, because there is a responsibility by the United States government for the situation of Mr. Alan Gross, so this is a topic, this is a matter, an issue that has to be discussed directly between Cuba and the United States in order to look for a solution.

BLITZER: And you're saying the U.S. is not ready to discuss Alan Gross' situation with Cuba? Is that what you're saying?

VIDAL: We have been waiting for a response and a reaction by the United States government to what we have conveyed about our willingness to sit down, to have a conversation and to initiate a negotiation on that matter.

BLITZER: We will continue this conversation, Josefina Vidal. Thank you so much for joining us and we will continue to talk. We'll stay in close touch.

VIDAL: It is my pleasure, Wolf. Thank you.