The Cuban grandmothers of 6-year-old Elian Gonzalez arrived here this afternoon to see their grandson for the first time since he was pulled from the sea on Thanksgiving Day. But after sitting at a south Miami airport for more than four hours this afternoon, they took off again without meeting the boy.

A day of confusion and rumors ended in dramatic fashion as Elian's great-uncle, Lazaro Gonzalez--without the boy--raced to the Tamiami Airport with television cameras in hot pursuit, only to see the plane taxi down the runway as he pulled up to the terminal.

Bob Edgar, the general secretary of the National Council of Churches, which sponsored the women's trip to this country, said after they departed that the grandmothers were traveling to Washington, where meetings were scheduled Tuesday with members of Congress.

The planned meeting with Elian fell apart in a dispute over where it would take place, with the Miami Gonzalezes insisting that the grandmothers, Mariela Gonzalez and Raquel Rodriguez, come to their turf in Little Havana, and the women saying they wanted to meet their grandson alone, on "neutral territory" at a location arranged by the Immigration and Naturalization Service.

Edgar said last night that the women were not confident of "security arrangements" in Little Havana. He said that the Miami relatives "did a cynical thing in telling a little boy they were going to have a party" with his grandmothers.

The rapid denouement came as hundreds of people, many of them Cuban Americans carrying largely friendly placards, along with police and reporters, had filled the streets this evening around Lazaro Gonzalez's Little Havana house where the boy has been staying.

Throughout the afternoon, after the grandmothers' plane touched down at about 3:45, INS attorneys had engaged in increasingly frantic telephone calls with attorneys for the Miami family in search of a compromise.

As relatives carried covered dishes into the house for a "family reunion" dinner with the grandmothers, Elian himself, freshly showered and dressed, was sent out to make an appearance in the front yard. Family spokesmen emerged to say rice and pork were on the table, and police tried to disperse the crowds.

By the time it was announced that Lazaro Gonzalez, and his brother, Delfin Gonzalez, were heading to the airport without the child to talk to the grandmothers, the women apparently had already made their decision.

The latest twist in the long Elian saga came as Congress entered with fray with the introduction of two bills to make the boy an instant U.S. citizen. One of the bills could be acted upon as early as Wednesday in the Senate. Although several historical figures have been made honorary citizens, Elian would be the first person ever naturalized by an act of Congress. President Clinton has not said whether he would sign such a bill, although White House spokesman Joe Lockhart said today that Clinton did not think Congress should be involved.

But the controversy appeared headed toward a largely partisan showdown, and Republicans and Democrats returning from the long holiday recess were expected to discuss Elian during party caucuses scheduled for Tuesday.

Sen. Christopher Dodd (D-Conn.) and Rep. Jose Serrano (D-N.Y.)--both strong supporters of sending Elian back to Cuba-- planned to host the grandmothers in meetings here with congressional colleagues.

Miami attorneys for the Gonzalez family, who sources said were acting on instructions from family spokesman Armando Gutierrez, had insisted that Elian's meeting with his grandmothers could only take place in Lazaro Gonzalez's Little Havana home.

A U.S. government official said that the women had said "they would not feel comfortable in that house," and that they considered the neighborhood, where feeling is strong against Cuba's communist government, to be filled with "animosity" toward them.

Elian has been staying with Lazaro Gonzalez since he was rescued from the shipwreck in which his mother and nine others drowned while trying to reach the United States. Although the INS ruled early this month that the boy should be returned to his divorced Cuban father, the Miami relatives have refused to relinquish him and have filed suit in state and federal court to retain him in this country.

The Justice Department expects to respond this week to the federal suit--in which Lazaro Gonzalez is seeking to force the INS to consider a petition he has filed to give Elian political asylum.

The two grandmothers, flown from Cuba to New York by the NCC Friday, visited Washington Saturday for a meeting with Attorney General Janet Reno and INS Commissioner Doris Meissner. Following that meeting, INS General Counsel Bo Cooper wrote to the Miami attorneys saying that the grandmothers wanted "to meet with Elian in a neutral, private setting during their brief stay in the United States," and would travel to Miami "if their safety could be ensured."

"The grandmothers understand," Cooper wrote, "that their meeting would only be a visit, and would not alter the present arrangements for Elian's care."

The Miami attorneys replied with a publicly released letter inviting the grandmothers to come to Little Havana at 6 p.m. for dinner where, Gutierrez said, they could see "where he sleeps, to see where he lives."

That offer was unacceptable to the women who, an official in Washington said, had no doubt Elian was being well cared for. "This is not a child welfare inspection," the official said. "They want to visit their grandson."

The women left New York on a charter flight today in the expectation that a compromise would be reached, officials in Washington said.

Pressley reported from Miami, DeYoung from Washington. Staff writer Helen Dewar in Washington and special correspondent Catharine Skipp in Miami contributed to this report.

CAPTION: Elian Gonzalez's grandmothers Mariela Gonzalez, second from left, and Raquel Rodriguez, third from left, depart from plane in Miami in hopes of meeting with him.

CAPTION: Elian Gonzalez waits for his great-uncle, Lazaro Gonzalez, to close the door of his home in Miami's Little Havana as they prepare to leave for school.