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A number of other dignitaries including foreign diplomats were killed or seriously wounded.
The Egyptian authorities have declared a state of emergency.
President Sadat was attending the eighth anniversary of the Yom Kippur war with Israel as Field Marshal of the armed forces.
He had taken the salute, laid a wreath and was watching a display from the Egyptian Air Force when two grenades exploded.
Gunmen then leapt from a military truck in front of the presidential reviewing stand and ran towards the spectators, raking officials with automatic gunfire.
Despite typically large numbers of security personnel for the ceremonial occasion, eyewitnesses say the attackers were able to keep shooting for well over a minute.
By the time the president's bodyguards returned fire at least ten people lay seriously injured or dead inside the stand.
Security forces then shot and killed two of the attackers and overpowered the rest, as crowds of military and civilian spectators scrambled for cover.
President Sadat was airlifted by helicopter to a military hospital. He is believed to have died about two hours later.
The precision with which the attack was coordinated has prompted suspicions that the attackers benefited from high-level intelligence and support.
A group calling itself the Independent Organisation for the Liberation of Egypt says it carried out the attack but the claim has not been verified.
Reaction to President's Sadat's death has been mixed.
President Reagan condemned Anwar Sadat's death as an act of infamy. Her said: "America has lost a great friend, the world has lost a great statesman, and mankind has lost a champion of peace."
But many have been celebrating the news. In Libya, Tripoli radio said every tyrant has an end, as thousands took to the streets of the capital in jubilation.
Neither has the Palestinian Liberation Organisation condemned the assassination. Nabil Ramlawi, a PLO official, said: "We were expecting this end of President Sadat because we are sure he was against the interests of his people, the Arab nations and the Palestinian people."
President Sadat was the first Arab leader to recognise the state of Israel since its creation in 1948.
Although popular in the West for his efforts at rapprochement with Israel, his policies dismayed much of the Arab world.
Under President Sadat, Egypt signed the Camp David accords with Israel in 1978 outlining "the framework for peace in the Middle East". This included limited autonomy for Palestinians.
A historic bilateral Egyptian-Israeli peace treaty was signed the following year. Arab states boycotted Egypt for breaking ranks and negotiating a separate treaty with Israel.
Following President Sadat's assassination, more than 700 people were rounded up.
Twenty-five faced a secret trial, five of whom were then executed, and 17 others given prison sentences and hard labour.
Vice-President Hosni Mubarak succeeded President Sadat as head of state.
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