By CNN's Jennifer Mikell
(CNN) – A top representative of the Castro government is urging the United States to sit down and talk about the fate of an American held prisoner in Cuba who reached out to CNN's Wolf Blitzer.
An international negotiation appears to be playing out in "The Situation Room", where high-level Cuban and U.S. officials are responding to Blitzer's exclusive interview with the jailed contractor, Alan Gross.
Gross used the one phone call the Cuban government allows him each week to contact Blitzer on Friday.
The 63-year-old Maryland contractor has served two-and-a-half years of a 15-year prison sentence in Cuba.
He talked to Blitzer about his life in captivity, his failing health and his 2009 arrest.
Gross and his family say he went to Cuba to link the island's tiny Jewish community to the internet, as part of a U.S.-funded aid program.
The Cuban government thought otherwise, charging Gross with smuggling in illegal equipment and with being a threat to the security and independence of the state.
Gross told Blitzer, "They charged me with smuggling. It's called 'contrabanda.' But that was impossible, because I had permission... I feel like I'm a hostage."
In fact, Gross’s lawyer suggests his client is effectively being held for ransom.
The Cuban government appears to have linked Gross' future to the fate of Cuban agents convicted on spy charges and imprisoned in the United States, known as "The Cuban Five."
The day after Blitzer's interview with Gross, the CNN anchor received a hand-delivered letter from a top Cuban diplomat in Washington, Jorge Balanos.
The letter outlined the Castro government's views on Gross' case, writing "The undercover activities of Mr. Gross in Cuba constitute crimes in many countries, including the United States."
Balanos began the letter saying, "The Cuban government has conveyed to the U.S. its willingness to have a dialogue to find a humanitarian solution to the case of Mr. Gross on a reciprocal basis."
Blitzer says that line in particular, and the full letter from Balanos, clearly suggested to him that Cuba is open to releasing Gross if the U.S. frees members of the Cuban Five.
Blitzer followed up, asking a top Cuban Foreign ministry official what it would take to free Alan Gross.
In a rare interview from Havana, Josefina Vidal told Blitzer that Cuba has "legitimate concerns, humanitarian concerns related to the situation of the Cuban Five." But she says Cuba is "not advancing a specific solution, a specific formula" for the release of Alan Gross. She said that has to be discussed with the U.S. government, and Cuba is waiting for a response from the Obama administration on the matter.
CNN asked Secretary of State Hillary Clinton about the possibility of a prisoner swap with Cuba.
Clinton told CNN's Jill Dougherty "well first of all Mr. Gross should not even be incarcerated in Cuba. Mr. Gross was not a spy, Mr. Gross was not an intelligence agent. So there should be a decision by the Cuban government to release him, and we would like to see that happen as soon as possible."
Clinton didn't directly reject a prisoner swap, but she noted, "we are well aware that the Cuban government wants to see the release of their intelligence agents." She referred to the Cuban Five as "spies who were lawfully arrested, tried and convicted for espionage."
A later statement from the State Department dismissed the idea of holding talks on Gross' fate. Deputy Spokesman Mark Toner wrote, "We reject the suggestion that this is a matter for negotiation. Alan Gross is unjustifiably imprisoned and his case is not related to the Cuban Five. Josefina Vidal's statements only seem to reinforce Alan Gross' view that he is a hostage of the Cuban regime."
In his interview with Blitzer, Gross praised efforts by Secretary of State Clinton and Pres. Obama to win his release.
Several world leaders have taken up the cause of Alan Gross.
Former President Jimmy Carter, U.S. Ambassador and former New Mexico Governor Bill Richardson and even Pope Benedict have all visited Cuba within the past year, calling on the government to release Gross.
The Chairman of the Senate Judiciary Committee, Patrick Leahy, visited Gross in Cuba and met with Cuban leader Raul Castro.
Blitzer asked Leahy about the possibility that Gross might be freed in a prisoner swap.
Leahy said, "I think you can make the argument that some of the Cubans have reached a point where they've served a long term, should they be returned."
"But I think if you go into it, we'll give you two if you'll give us one, we'll give you three if you give us one, that's a non-starter. We ought to talk first humanitarian. And we ought to talk to the long, bigger issues of relationships between our countries."
In his letter to Blitzer, the Cuban diplomat Jorge Balanos said the cases of Alan Gross and the Cuban Five are very different, arguing that they have endured a "cruel regime of solitary confinement" during nearly 14 years in U.S. prisons.
Blitzer is determined to keep the lines of communication open between the U.S. and Cuba on this important story. Be sure to watch "The Situation Room" for follow-up reports. That's 4-6 p.m. ET, only on CNN.
RELATED VIDEO: Wolf Blitzer's full interview with Josefina Vidal