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Thousands of students had gathered for a meeting organised by the National Strike Council in La Plaza de las Tres Culturas in Tlatelolco to protest against the military occupation of the National Polytechnic Institute.
The protesters, many of whom were women and children, had been planning to march through a working-class suburb of the city, but by early evening military personnel in armoured vehicles had surrounded the square.
The Mexican government say "agitator groups" among the students began shooting at the crowds from buildings, which resulted in a 90-minute gun fight.
General Marcelino Garcia Barragan, Mexico's defence minister said the army began firing into the crowd in self-defence after they found themselves targets of sniper fire from buildings in the square.
But several eye-witnesses claim the army entered the square in seven or eight armoured tanks and began shooting first.
After the fighting had subsided dozens of bodies lay strewn across the square, many more were injured.
More than 500 people have been arrested.
The violence follows weeks of demonstrations by students demanding democratic reform and social justice. They have used the international focus on Mexico City because of the Olympics to promote their message.
In September, President Gustavo Díaz Ordaz, in a bid to suppress the protests and cause minimum disruption to the Olympics, ordered the military occupation of the National Polytechnic Institute in Mexico City.
At this stage it is not clear whether the 7,000 athletes, currently preparing for the Games 11 miles away from Tlatelolco in the Olympic Village, are in danger. It is the first time the Olympics have been held in a Latin American country.
Lord Exeter, British vice-president of the International Olympic Committee told the Times: "The riots have nothing to do with the Olympic Games. The students are not protesting against the games but against the Mexican government."
Following the massacre the Mexican government, facing one of its worst crises ever, launched a huge cover-up operation.
The death-toll still remains uncertain. Some say it runs into thousands although it is thought to be between 200 and 300. Eye-witnesses say bodies were removed from the scene throughout the night of 2 October in dustbin lorries.
The following day, Avery Brundage, president of the International Olympic Committee, said the Olympics would go ahead, saying none of the violence had ever been directed towards the Olympics.
In October 2003 it emerged that America had played a key role in the massacre.
Amidst fears the riots would disrupt the Olympic Games the CIA had been monitoring the student actions in Mexico daily. As a result they sent military radios, weapons, ammunition and riot control training material to Mexico before and during the crisis.
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