MIAMI (CNN) -- With the U.S. government threatening to quickly repatriate
                  the boy to Cuba if his Florida relatives don't speed up action on his court
                  appeal, family members said on Sunday they have allowed 6-year-old Elian
                  Gonzalez to be interviewed by a U.S. television network.

                  ABC News's Diane Sawyer interviewed Elian Gonzalez this week, said Roger
                  Bernstein and Linda Osberg-Braun, attorneys for Miami relatives of the
                  6-year-old boy. They said they did not know when the interview would be
                  broadcast.

                  The lawyers were planning to meet with the family on Sunday.

                  On Tuesday, U.S. District Judge K. Michael Moore's threw out a political
                  asylum lawsuit filed on Elian's behalf, clearing the way for implementation
                  of an Immigration and Naturalization order that the boy be returned to his
                  father in Cuba.

                  Hours after the ruling, the lawyers for the boy's Miami relatives filed a notice
                  of their intention to appeal the decision.

                  The Justice Department late Friday told the relatives that they have until noon
                  Monday to agree to quickly resolve that appeal or the boy will be swiftly
                  returned to his father, according to family spokesman Armando Gutierrez.

                  The government wants the attorneys to confirm their intention to file legal
                  briefs before the 11th Circuit Court of Appeals in Atlanta by April 3. If they
                  miss the deadline, the Justice Department says it will take steps to revoke the
                  boy's temporary custody status on Thursday.

                  Attorney General Janet Reno issued a written statement late Friday, saying
                  the Justice Department is "not willing to wait through an open-ended appeals
                  process that could prolong separation of this child from his father."

                  "We cannot risk the harm that a prolonged separation might create," Reno
                  said.

                  "From the beginning, we have been mindful of the fact that at the center of
                  this case is a 6-year-old boy who has been through a terrible ordeal. We are
                  concerned for him and will continue to try to resolve this matter in a way that
                  avoids additional trauma to him."

                  Reno said the government has proposed a solution that allows Elian's Miami
                  relatives adequate opportunity to appeal their case, while "working to achieve
                  a reunion between Elian and his father."

                  Elian may be turned over to INS by Tuesday

                  Federal attorneys originally had given the boy's relatives until noon on Friday
                  to agree to speed up the appeals process. They also were asked to commit to
                  quickly returning Elian to his father, Juan Miguel Gonzalez, if their appeal
                  failed.

                  Reno said the Justice Department had sent a letter to the attorneys for the
                  Miami relatives on "setting forth the next steps." She did not elaborate on what
                  those steps were.

                  Osberg-Braun said the letter warned that if the legal team does not comply
                  with the request for an expedited appeal, Elian's temporary status in the
                  United States will be revoked Thursday, March 30.

                  The boy would have to be presented in person Tuesday to INS officials in
                  Miami to make arrangements for his repatriation to Cuba.

                  Boy's father wants him back

                  Elian has been living with his great uncle Lazaro Gonzalez in Miami since late
                  November, when he was found floating on an inner tube off the Florida coast.
                  His mother and 10 others drowned after their boat capsized en route from
                  Cuba to Florida.

                  Elian's father, a hotel worker who was divorced from his mother, has
                  demanded his son be returned to him.

                  Elian's Florida family has fought to keep in the United States and Miami's
                  Cuban exile community has adopted Elian as a symbol of their struggle against
                  Cuban President Fidel Castro.

                  Castro, meanwhile, has led massive demonstrations demanding that Elian be
                  returned to Cuba.

                  The most recent protest occurred on Saturday, as state media reported an
                  estimated 50,000 demonstrators gathered in the city of Sagua la Grande to
                  demand that the 6-year-old be returned to his father.

                  Government television broadcast the event live, and showed tens of thousands
                  of people wearing T-shirts featuring Elian's portrait and waving Cuban flags.

                  Legal team proposed arbitration

                  Osberg-Braun said lead appeals attorney Kendall Coffey is working on a
                  response to the government. The lawyers responded to the government's
                  earlier ultimatum by counter-proposing that an arbitration panel decide "the
                  best interests of the child."

                  U.S. Immigration and Naturalization Commissioner Doris Meissner flatly
                  rejected that proposal.

                  "That is not an option I'm prepared to entertain," Meissner said Friday. "There
                  is no place for an arbitration panel."

                  Meissner said her decision to send Elian back to Cuba at his father's request
                  was "within my discretion" and is now upheld by a federal court.

                  Lawyers representing the boy's Miami family had offered arbitration as an
                  alternative to the lengthy appeals process that they have vowed to take all the
                  way to the Supreme Court.

                  The attorneys said they would work with the INS in selecting the arbitrator,
                  suggesting former Sen. Bob Dole or former Sen. George Mitchell for the
                  position.

                  "If the INS would agree at last to provide a day in court to this small child, the
                  result would be not only a fair determination of what's right for Elian, but a
                  much faster resolution than is possible through further court battles," the
                  attorneys wrote.

                  Exile community on alert

                  Cuban-Americans make up more than 700,000 of Miami-Dade County's 2.1
                  million people. Many harbor a deep-seated hatred of Castro and have held
                  several protests against the INS ruling to send Elian back to Cuba.

                  Ramon Saul Sanchez, leader of the Democracy Movement anti-Castro group,
                  said Cuban American supporters of the boy's Florida relatives were on "full
                  alert" for any sudden action by the government to repatriate Elian.

                  "In that case, we'll call people out to demonstrate," said Sanchez, who lead
                  some Miami protests in January.

                  Some exiles fear a squad of U.S. marshals might try to seize Elian from his
                  great-uncle's house, despite assurances to the contrary by U.S. officials.

                  The boy's father has said in the past he would come to the United States to
                  collect his son, but not to become embroiled in a court case.

                               The Associated Press and Reuters contributed to this report.