The U.S. government yesterday ordered that Elian Gonzalez, the 6-year-old boy who has been at the center of an international tug of war, be returned to his Cuban father within the next 10 days.

Immigration and Naturalization Service Commissioner Doris Meissner said that an INS investigation has not found "any information that might call into question" the father's parental and legal rights. She urged "everyone involved to understand, respect and uphold the bond between parent and child and the laws of the United States."

"This little boy, who has been through so much, belongs with his father," she told a news conference at INS headquarters.

But an early end to the six-week-old controversy remained in question, as Cuban American relatives in Miami who have vowed to keep the boy said yesterday that they would fight the ruling.

Neither the Cuban government nor the boy's father--invited yesterday by the INS to pick up his son--publicly responded to Meissner's statement. Havana officials said they were studying the decision and waiting to see what would happen in southern Florida.

At a late afternoon Miami news conference after sporadic, but relatively small demonstrations there, attorneys for the relatives released a letter to Attorney General Janet Reno asking that she "review and reverse" what they called an "unfair and unconstitutional" ruling. They asked that she take the matter out of INS hands and "consult with the President of the United States."

Such action appeared unlikely, however, as a Justice Department spokesman noted that the INS had closely consulted with Reno. In comments on the White House lawn, President Clinton said the administration had kept the deliberations "out of politics" and that he was "convinced [the INS] followed the law and the facts [and] did the best they could with the decision."

In the event Washington does not respond positively, Miami lawyer Spencer Eig said, members of the legal team have "prepared and are ready to file various federal and state writs to protect Elian's constitutional rights."

U.S. officials have said that the Justice Department would contest in court any effort to overturn the decision and have expressed confidence they would prevail.

Several hundred protesters were waiting outside the Miami INS headquarters yesterday morning as the relatives were officially informed of the decision. Later, leaders of several organizations opposed to Cuba's communist government joined demonstrators outside the home of the child's great-uncle, Lazaro Gonzalez, in Miami's Little Havana. Ramon Saul Sanchez, leader of the Democracy Movement, said a protest rally has been scheduled for noon today in front of the Claude Pepper Federal Building in downtown Miami.

The child has been staying with Lazaro Gonzalez since he was found adrift off the Florida coast after a shipwreck in which his mother and nine other Cubans fleeing their homeland drowned. Relatives have rejected demands by his divorced father and the Cuban government that he be sent home, saying he would have a better life in the United States.

Elian attended his second day of kindergarten yesterday in a school chosen by his relatives. A family spokesman, Armando Gutierrez, said he had taken the child "someplace for the rest of the day" to avoid the crowds and the excitement.

INS officials informed the father, Juan Miguel Gonzalez, of the decision by telephone in his hometown of Cardenas, two hours east of Havana. For the first time, Meissner said in an interview, they asked him directly if he would be willing to retrieve his son in Miami. His response, she said, "was left open."

Juan Gonzalez had said in the past that it was the United States' responsibility to return Elian, and that he saw no reason to travel to this country. The Cuban government, while insisting that the decision was up to Gonzalez, had said there was no point to such a trip until the INS has made a decision.

U.S. officials agree that the possibility of court action complicates what could be a smooth resolution of the matter--and is the basis for the hesitation by both Juan Gonzalez and the government in Havana. Such action could take several forms. Attorneys for the relatives have threatened to take the matter to Florida family court to ask for custody on grounds that the father is not acting in the child's best interests. They maintain that the Cuban government is pressuring the father to insist that he wants Elian home.

According to a number of family and immigration law experts, however, Florida state courts have no jurisdiction in the case.

Administration officials take more seriously the threat to appeal the matter to federal court, where lawyers could ask for a temporary restraining order against the INS ruling. Such orders are routinely granted for 24 to 48 hours, after which the Justice Department would argue against a permanent injunction.

The United States maintains that the relatives have no standing in the case and that there is no reason for the courts to intervene. In the event the relatives appeal a decision against them, the Justice Department is prepared to ask the U.S. Court of Appeals to address the issue on an emergency basis.

All of this, Meissner said yesterday, could be taken care of by the Jan. 14 deadline she has set for Elian's return home--although she said that his father is now free to pick him up at any time.

Above all, the administration is strenuously seeking to avoid having to send the U.S. Border Patrol or U.S. marshals to forcibly extricate Elian from Miami.

In her statement yesterday, Meissner explained at length the procedures the INS had gone through to make a determination in the case, and said "it is our hope . . . the Miami relatives will agree to cooperate and work together . . . to facilitate Elian's return to his father."

Under U.S. law, any Cuban is eligible to apply for permanent residence upon reaching this country. Because Elian is "too young to make legal decisions for himself," she said, the only question before the INS was who could legally represent him in deciding whether to make that application.

"There is no question that Mr. Gonzalez is Elian's father," Meissner said. "Moreover, Mr. Gonzalez has had a close and continuous parental relationship with his son" despite the divorce of his parents. In two interviews with INS officials, Gonzalez "provided vivid details about his parental relationship . . . and about the nature of the bond they share as father and son."

The extensive documentation of Elian's school and medical histories that he provided, as well as numerous photographs of the activities Elian had shared with his father and other family members in Cuba, informed the INS "as to the nature and closeness of their relationship," she said.

Responding to charges in Miami that Gonzalez has been speaking under duress from the Cuban government, Meissner said that Gonzalez's "wishes for Elian were discussed at some length" during the INS meetings. "He made it very clear . . . that he wants Elian returned to him as soon as possible.

"INS believes that he is expressing his true wishes, and therefore we have determined that Elian should be reunited with his father."

If Gonzalez chooses not to come to pick him up, Meissner said, "INS also has offered Elian's great uncle in Miami . . . an opportunity to escort Elian back to Cuba." Officials also are willing to work with third parties that have offered to facilitate his return, including the National Council of Churches.

"Both U.S. and international law recognize the unique relationship between parent and child, and family reunification has long been a cornerstone of both American immigration law and INS practice," Meissner said.

Urging all involved to cooperate, she said, "We believe this decision can be carried out without INS' taking charge of Elian."

DeYoung reported from Washington and Pressley reported from Miami. Special correspondent Catherine Skipp also contributed to this report.

CAPTION: Elian Gonzalez is held by his great-uncle, Lazaro Gonzalez, as he shares a laugh with Lincoln Marti staff members after leaving class on his second day at the Little Havana school in Miami.

CAPTION: Outside the home where Elian Gonzalez is staying, demonstrators rally in support of the efforts of the boy's relatives to keep him.

CAPTION: Elian, 6, walks to school in Miami with cousin Marisleysis Gonzalez. U.S. officials have decided that Elian should be returned to his father in Cuba.