Sen. Orrin Hatch, R-Utah, Senate Judiciary Committee chairman, said the dispute ``is not just a custody matter, but a case where one of the options considered is returning this child to one of the last prison nations in the world.''
But Sen. Patrick Leahy of Vermont, the panel's senior Democrat, said the committee was making a mistake trying to intervene in an immigration case that is currently before a federal court in Miami.
``A young boy belongs with his parent, not with distant relatives,'' said Leahy. ``Because we all oppose Fidel Castro does not mean we should oppose this boy being with his father.''
Congress is considering legislation by Sen. Connie Mack, R-Fla., that would confer citizenship on the 6-year-old shipwreck victim.
The Committee heard from the boy's Miami-based relatives and Alina Fernandez, the daughter of Cuban leader Fidel Castro. Fernandez, Castro's out-of-wedlock daughter who fled the country in 1993, is one of her father's fiercest critics, and she said Elian should stay in the United States.
Fernandez told the panel: ``You cannot allow this unilateral victory on behalf of a dictator.''
``Parental rights, family rights, do not exist there,'' she said of Cuba. Elian's family there``is being used and manipulated by the Cuban government for political purposes and to generate anti-American sentiment,'' Fernandez asserted.
Testifying before the committee, Elian's surrogate mother, 20-year-old cousin Marisleysis Gonzalez, said she believes the boy's father really wants to come to the United States himself, but can't. "He tells me that he thanks me for everything I'm doing for his son."
"He himself stated to my father, 'Please take care of him until I'm able to come over there,' because for three months nobody's allowed him to come over to this country."
Sometimes crying, Gonzalez said the boy knows what he wants, and has told his father by telephone that he wants to stay in the United States, reported CBS News Correspondent Dan Raviv.
"He got very hyper. And he told his father, 'If you do not know, my mother drowned, and I am not going to go back over there,'" she testified.
The boy has been the center of an international custody dispute since he was found clinging to an inner tube on Thanksgiving Day off the Florida coast. His mother and 10 others traveling with him drowned in an effort to flee Cuba. He is currently staying with his Miami relatives.
Last month Senate Democratic Leader Tom Daschle suggested that sentiment is growing in both parties in the Senate for allowing the boy to return to his father in Cuba.
Senate Majority Leader Trent Lott, R-Miss., had once pledged to bring a bill confrring U.S. citizenship on the boy to a quick Senate vote but backed away from the plans.
The boy's two grandmothers made personal appeals to allow Elian to be returned to Cuba in visits earlier this year to members of Congress.
Lazaro Gonzalez, another great uncle, has sued the Immigration and Naturalization Service in federal court and challenged the agency's decision to send the boy back to Cuba.
U.S. District Judge K. Michael Moore plans to hear arguments in the federal case next week.