The decision will be posted on the World Wide Web.
The boy's Miami relatives have pleaded to U.S. District Judge K. Michael Moore for the right to seek asylum for the child who was found floating in an inner tube last November while fleeing Cuba with his mother; she drowned during the escape.
Spencer Eig, one of the attorneys for Elian's Miami family, said the hearing went well.
"We were very pleased. The judge was well informed," Eig said. "Elian has the right to a review of his political asylum application because, if returned to Cuba as a high-profile political symbol, he will be exposed to a tremendous risk there."
But lawyers for the U.S. Immigration and Naturalization Service argued the only person who can speak for Elian is his father.
"It is our hope that the court... will make it possible for this little boy to go home to his father and bring an end to this extraordinary case," said Patricia Maher of the Department of Justice.
Eig said if immigration is going to rely on the boy's father to make their case then he should come to the U.S. and testify in person.
"If the INS wants to rely on a affidavit given by an individual in Cuba who has no freedom and who is under the thumb of the regime and who is a tremendous risk himself, it's important that we know exactly what safeguards and procedures they undertook," Eig said. "They say they had (the interview) in a safe house. But even in Cuba, a person has to come out of the house."
Eig has subpoenaed the INS personnel who interviewed Elian's father in Cuba.
Meantime, there is another sign this international custody dispute is drawing to an end.
Washington attorney Gregory Craig, the same lawyer who represented President Clinton during his impeachment trial, has been hired to represent Juan Gonzalez, Elian's father.
This suggests, sources say, that Gonzalez is preparing to come to the U.S. and reclaim his son. In the opinion of legal experts like Pamela Falk of New York University Law School, the endgame has begun.
"It's now been just over a hundred days," Falk says, "since a little boy lost his mother, and found himself caught between the Cold War passions and politics of two countries."
Relatives of Elian Gonzalez in Miami say they have raised $215,000 for their legal fight to keep the boy in this country.
More than $200,000 was raised through a radio marathon Saturday on four Spanish-language stations, family spokesman, Armando Gutierrez, said Sunday. Those donations were added to $15,000 raised earlier in the week.
"We're gettin all kinds of donations," Gutierrez said. "And we really haven't advertised it outside Miami-Dade County."