MIAMI (CNN) -- U.S. Immigration and Naturalization Commissioner Doris
                  Meissner on Friday swiftly rejected a proposal from Elian Gonzalez's Miami
                  relatives that the 6-year-old Cuban boy's custody case be arbitrated rather
                  than appealed through the U.S. courts.

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

                  The Miami family's proposal was made around midday Friday as members
                  rejected a U.S. Justice Department request, made late Thursday, to speed up
                  their court fight over custody of the boy.

                  The proposal for arbitration came as lawyers representing the boy's Miami
                  family met Friday to consider whether to meet the Justice Department's noon
                  deadline to speed up the appeals process or risk having the boy quickly
                  returned home to his father in Cuba.

                  Instead of agreeing to speed up the process, the lawyers said they are willing
                  to give up their right to file an appeal with the 11th U.S. Circuit Court of
                  Appeals in Atlanta if the goverment agreed to arbitration.

                  A letter, sent by the Justice Department to lawyers of the boy's Miami family,
                  had asked for an "expedited briefing schedule" for an appeal of a federal court
                  decision against them.

                  "This is a step in the process to move forward to quickly reunite Elian and his
                  father," an INS official had told CNN.

                  Officials had said that an expedited schedule would shorten the appeals process
                  to two to three weeks, rather than two to three months.

                  The INS in January ordered that Elian be returned to his father, Juan Miguel
                  Gonzalez, in Cuba. He now lives with his great-uncle in Miami's Little Havana.
                  The Miami relatives responded to the INS ruling with a lawsuit that was
                  dismissed on Tuesday.

                  The boy's mother, who was divorced from Gonzalez, drowned along with 10
                  others when their boat capsized off the coast of Florida in November as they
                  tried to make it to the United States.

                  Elian was rescued and two others survived. He quickly became the center of
                  a custody dispute between relatives in Miami's Cuban-American community
                  and his father and grandparents in Cuba. The issue escalated into an
                  international dispute.

                  Wishes of 'surviving parent'

                   U.S. District Judge K. Michael Moore threw out the lawsuit filed on behalf
                   of Elian's Miami relatives. His ruling upheld Attorney General Janet Reno's
                   authority giving Elian's father sole legal authority to speak for his son and,
                   therefore, to withdraw an application for asylum in the United States filed
                   on Elian's behalf by his great-uncle.

                  "As a general matter, when dealing with a child this young, the immigration
                  law, like other areas of law, looks to the wishes of the surviving parent,"
                  Moore said.

                  "I am not currently aware of any basis for reversing (INS Commissioner
                  Doris) Meissmer's decision that Juan Gonzalez, Elian's father, has the sole
                  authority to speak for his son on immigration matters," he said.

                  Cuban-Americans keep watch over home

                  Members of Miami's large Cuban-American community, some with
                  walkie-talkies, have been keeping close watch on Elian's Florida home and
                  threatening protests if the U.S. government makes any sudden move to send
                  the boy back to Cuba.

                  "We're not calling the people out as long as we see that Elian's case remains
                  in the courts and the government is not moving to suddenly take Elian back to
                  Cuba," said Ramon Saul Sanchez, head of the Democracy Movement, a
                  Cuban exile organization.

                  "We have used civil disobedience in the past, but only when it has been
                  absolutely necessary," Sanchez said.

                  He said preserving Elian's rights and maintaining peace in the community was
                  a delicate balance. "There are things we can control and there are certain
                  things we can't control. There are very, very deep emotions involved here and
                  people will react."

                  Cuban-Americans make up more than 700,000 of Miami-Dade County's 2.1
                  million people. Many harbor a deep hatred of Cuban leader Fidel Castro and
                  have shown their willingness to take to the streets in protest.

                                  The Associated Press contributed to this report.