The judge did not reach a decision or announce when he will reconvene the proceedings.
U.S. District Judge Michael Moore must decide whether Elian's great-uncles can legally challenge an INS ruling that Elian be returned to his father, reports CBS News Correspondent Vince Gonzalez.
The lawsuit filed by Lazaro Gonzalez also seeks a political asylum hearing for the boy.
About 60 flag-waving demonstrators snarled traffic outside the courthouse. Most support Elian's staying in the United States. Police had to separate a group arguing with a Miami-Dade Community College student who thinks Elian should be returned to his father.
The I.N.S., backed by President Clinton and Attorney General Janet Reno, says the boy should be returned to his father in Cuba. His relatives in Miami say he should be given asylum in this country and they already have won a victory in Florida state court.
The lawsuit also seeks a political asylum hearing for the boy.
Legal experts worry that any ruling that keeps Elian in the U.S. could set a dangerous precedent.
"If we do not reunite Elian with his father, we are not only doing great damage to immigration law, but we are also doing great damage to long established principles of American family law," says Pamela Falk of New York University Law School.
Elian's lawyers will argue his mother died trying to get him out of Cuba, and they are ready to fight to have her last wishes honored.
But the arrival in Miami of another wing or the family has added a new element. They also are suing for custody, but if they get it, they are saying they'll send him back to his father in Cuba.
On Wednesday night, Cuban President Fidel Castro blamed U.S. immigration policies for Elian's plight.
Speaking for the first time at one of the scores of mass protests held in Cuba almost daily since Dec. 5, Castro described the Cuban Adjustment Act as a "monstrosity" that lures Cubans to risk the lives of themselves and their children.
The law, passed in 1966, allows Cubans who reach American soil to stay and apply for political asylum.
"How many lives has this law cost our nation? How many lives of innocent children pulled out of school by mothers or fathers who are irresponsible or tricked by illusions?" Castro said.
Last week, the boy's father, Juan Miguel Gonzalez, met with U.S. lawyer Gregory Craig, who represented President Clinton during his impeachment and trial. Craig will represent Gonzalez in his efforts to reunite with Elian, the Washington Post has reported.
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