NEW YORK, Oct. 23, (WP) -- Thousands of demonstrators gathered near the United Nations today to draw attention to human rights violations they say the organization is ignoring around the globe.

As heads of state addressed the General Assembly at the United Nations' 50th anniversary, some 6,000 protesters marched through Manhattan to Dag Hammarskjold Plaza, cordoned off from the U.N. building.

They waved posters and banners, handed out leaflets and videos and lent each other their support, with Cubans cheering along with Tibetans against China.

"It's ridiculous to put us all here and put all the leaders three or four blocks away," said a man protesting against Sri Lanka's treatment of Tamils in that country.

Organizers said they hoped the United Nations would consider their cases during the 50th anniversary summit, but there was no sign that any U.N. delegates were paying attention to their rallies, some of which included demonstrators bused in from Canada or flown in from Japan.

Tibetans, Tamils and Cubans opposing President Fidel Castro dominated the demonstration but other protests were against Japan, Zaire, Vietnam, Pakistan, Belarus and Taiwan.

Castro's daughter, Alina Fernandez Revuelta, spoke briefly, denouncing her father as a tyrant and a terrorist, while demonstrators signed petitions in support of the U.S. embargo against Cuba and waved signs saying "No Castro, No Problem". Revuelta left after her speech, blowing kisses to Cuban-Americans as they shouted, "We love you."

Joseph Mendez, 25, a Cuban exile living in Weehawken, N.J., said he wanted to speak for his family still in Cuba "because they aren't allowed to speak out."

"If you see Fidel Castro, shoot him in the head. Fidel Castro should be shot, not defended by the New York City Police," he shouted through a megaphone.

Six Tibetan protesters who have been on a hunger strike since Oct. 14 remained silent, lying under blankets on a row on mattresses.

A doctor examined the protesters Saturday and found that the only female demonstrator, Yiga, 26, was in serious condition, said Namkha Tenzin, general secretary of the National Democratic Party of Tibet.

Supporters offered prayers and traditional white scarves. Hundreds of demonstrators in yellow bibs and headbands chanted nearby for the United Nations to give the Dalai Lama a seat and ultimately to rid the Buddhist state of Chinese rule imposed in 1959.

"If I die, then it's the U.N.'s shame," said the youngest hunger striker, 23-year-old Tenzin Dangsong.