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The surfer, a man aged 28, lost a leg in the attack and was pronounced dead on being brought back to the port of Saint-Leu in the west of the island, emergency services told AFP.
The "surfer was accompanied by three friends who tried to take him back to land but did not manage," said Olivier Tainturier, a senior local official in the nearby town of Saint-Paul.
A sharp increase in shark attacks on Reunion since 2011 has been dubbed locally the "shark crisis" and prompted authorities to step up alert systems.
It is the 24th shark attack recorded since 2011 on the island, which is French territory, and the 11th one to result in a fatality. As after previous attacks, operations have started to catch sharks in the waters of the incident.
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Before the latest attack, the local authorities had urged the "greatest vigilance" among beach users as more people flock to the coast at a season when there are high numbers of the highly aggressive bull shark.