MIAMI (CNN) -- The tug-of-war over Elian Gonzalez has turned into a waiting
                  game, with two federal courts considering the boy's fate and protesters in Little
                  Havana maintaining an uneasy vigil in the streets around the home where the
                  child is staying.

                  The next move is expected to come from the 11th U.S. Circuit Court of Appeals in
                  Atlanta, which issued an injunction Thursday temporarily blocking the 6-year-old
                  boy from being taken out of the country.

                  The government has asked the court to rescind that decision and to order Elian's great-
                  uncle Lazaro Gonzalez to end his four-and-a-half month custody struggle by surrendering
                  the boy.

                  There was no indication when the three-judge panel might reach a decision.

                  While the lawyers and the boy's relatives waited for the courts to act, protesters continued
                  their vigil outside Lazaro Gonzalez's home Saturday, holding up colorful posters, singing,
                  praying and giving speeches in front of the dozens of media cameras staking out the
                  Gonzalez house.

                  The protesters have repeatedly promised to form a human chain to block federal agents
                  from seizing Elian.

                  Elian slept in, and didn't appear in the yard until after 1 p.m. for what has become a
                  daily combination of playtime and media photo opportunity.

                  How long will Elian stay?

                  It remains unclear if or when Elian will leave the United States. The government,
                  in the appeals court filings, said Elian's father, Juan Miguel Gonzalez, has agreed --
                  if he gets custody -- to stay in the United States until appeals in the case are resolved.

                  But Miami Mayor Joe Carollo on Saturday openly questioned that pledge.

                  "What real guarantees do we have, since the Cuban government is an outlawed
                  government that has no word, that the minute this boy is given over to
                  them...that within a very short time they're not going to hide him in a vehicle,
                  take him to the nearest airport and fly him back to Cuba," Carollo told CNN.

                  The boy's father, who came to Washington on April 6 in hopes of reclaiming his
                  son and bringing him back to Cuba, visited the National Cathedral on Friday and
                  said he was frustrated with the repeated delays in the case.

                  Juan Gonzalez on Saturday left the home of the Cuban diplomat near Washington
                  where he has been staying for more than a week to visit the offices of his
                  lawyer.

                  Father: 'I'm going back with him'

                 Meanwhile, in an apparent attempt to speed up Elian's reunion with his father,
                                               U.S. immigration authorities have issued
                                               their own order blocking Elian from
                                               leaving the United States. That order,
                                               officials said, would take effect only
                                               when Elian's great-uncle voluntarily
                                               transfers the boy to his father.

                  The Immigration and Naturalization Service sent a letter to Juan Gonzalez advising
                  him that his son, Elian, must remain on U.S. soil while a federal court considers an
                  appeal seeking a political asylum hearing for the boy.

                  "The INS has determined that the departure of your son Elian Gonzalez would be
                  prejudicial to the interests of the United States," the letter said.

                  However, INS spokeswoman Maria Cardona told CNN, that if the government
                  must retrieve Elian without the cooperation of the Miami relatives, Juan Gonzalez
                  would be free to leave the United States with Elian at any time, Cardona said.

                  The letter to Elian's father, signed by Robert Wallis, district director in Miami of
                  the INS, concludes, "We understand that you do not oppose this order."

                  Elian's father, who came with hopes of a quick return to Cuba with his son, told
                  CNN he feels frustrated but still hopeful. "All I can do is to wait, keep waiting,"
                  he said in Washington.

                  Asked how long he thought he might have to wait, Juan Gonzalez shrugged his
                  shoulders.

                  When he was asked by a Spanish-speaking reporter if he would return to Cuba
                  without Elian, Juan Gonzalez smiled, gave a thumbs-up sign and said, "I'm going
                  back with him."

                  Government calls great-uncle 'mere distant relative'

                  At issue in the flurry of briefs is an emergency injunction from the federal
                  court in Atlanta issued Thursday at the Miami family's request.

                  It temporarily blocked anyone from taking Elian out of the United States until
                  the court hears arguments from the Miami relatives, who want the boy given
                  political asylum in the United States. A lower court upheld an INS ruling that
                  only the father could seek an asylum hearing for Elian. An appeals court hearing
                  on that asylum request is due next month.

                  Before that, though, the three-judge appellate panel in Atlanta must rule on the
                  Miami's family's bid to prevent Elian's return to Cuba with his father -- in other
                  words, whether to uphold or reject the temporary injunction.

                  In its reply, the government said Lazaro Gonzalez had violated a federal order to
                  surrender the boy on Thursday.

                  "There's no basis to prevent the reunion of a father and son at the behest of a
                  mere distant relative into whose care Elian was only temporarily placed under
                  federal law," the government attorneys said in their brief.

                  That was a reference to Lazaro Gonzalez, Elian's great-uncle who has had
                  temporary custody of the boy.

                  The brief singled out Lazaro Gonzalez, saying he comes to the court "with very
                  unclean hands" for defying an INS directive to transfer custody of the boy
                  Thursday at a Miami-area airport, despite a personal, face-to- face appeal from
                  Attorney General Janet Reno.

                  Clinton: The law is the law for everyone

                  President Clinton on Saturday said he had spoken with Reno about the case
                  when she returned from Miami.

                  "We have to let the court cases be decided but I think the main thing is I hope
                  that all the people there who say they came to the United States because we have
                  freedom and the rule of law will observe the rule of law," Clinton said.

                  He also reaffirmed his confidence in Reno's handling of the case.

                  "She was a prosecutor there for 12 years, so she knows it very well and
                  she's down there working hard on it and I think she'll handle it in as sensitive
                  -- but firm -- a way as possible," he said.

                  New legal angle invokes U.N. human rights charter

                  In another federal court in Washington, attorneys for Elian's Miami relatives have
                  argued that the boy should be barred from leaving the United States until the U.S.
                  government can certify that his human rights would not be violated if he returned
                  to Cuba.

                  In Cuba, "Elian would face the risk of being persecuted for having sought
                  asylum in the United States," lawyers for his great-uncle Lazaro Gonzalez said in
                  papers filed Thursday.

                  The attorneys also alleged Elian would be indoctrinated to believe his mother, her
                  boyfriend and his family in Florida were "traitors to the revolution."

                  They asked that the U.S. government to be barred from deporting Elian unless
                  the State Department can certify that Cuba is in compliance with the U.N.
                  Declaration of Human Rights and that the country is "no longer engaged in
                  systematic, gross violations of human rights."

                  A judge set a meeting with lawyers for Wednesday to discuss whether the case
                  will go forward.

                  As the legal maneuvers play out, the government is not prevented from removing
                  Elian from the home in Miami's Little Havana neighborhood where he has lived
                  since his rescue at sea more than four months ago.

                  Only a handful of demonstrators stood watch in the rain outside that house
                  Friday. Thousands had gathered the day before, with many shouting defiance of
                  any government effort to remove the boy.

                  Father visits Washington churches for prayers

                  Elian has been living with his Miami relatives since he was picked up floating on
                  an inner tube off Florida's coast last November. The child's mother and 10
                  others drowned when their boat sank on a migrant voyage from Cuba. Elian was
                  one of three survivors.

                  INS Commissioner Doris Meissner said Friday the U.S. government had done
                  everything it could to reunite the boy with his father, who is becoming
                  increasingly impatient with the American legal process.

                  She said the Elian Gonzalez case was a family matter between a father, a son and
                  relatives who had become attached to the boy.

                  Juan Gonzalez, who came to Washington on April 6, made prayer stops Friday at
                  two churches in the capital. He first went to the National Cathedral for "private
                  prayer and contemplation," according to a spokeswoman for the cathedral.

                  Later, the father and his supporters attended an ecumenical prayer gathering at
                  the United Methodist Building in Washington.

                  Juan Gonzalez, his second wife and their infant son have been staying in the
                  Washington suburb of Bethesda, Maryland.

                    Havana Bureau Chief Lucia Newman, Justice Department Correspondent Pierre
                  Thomas, Susan Candiotti, and Bob Franken, Bill Delaney, and The Associated Press
                                      contributed to this report.