Devotees believe the shroud, which is imprinted with the image of a man who appears to have been crucified, to be the burial cloth of Jesus Christ.
Sceptics are just as adamant that it is nothing more than a Medieval forgery which scientists have carbon-dated to around 1300 years after Christ supposedly died on the cross.
Despite their certainty about the likely age of the most-talked-about length of linen in history, researchers have not been able to explain how the remarkable image was created, leaving space for theories of some sort of miraculous process to flourish.
The Church does not officially maintain that Christ's body was wrapped in the shroud or that the image was the product of a miracle.
But it does accord the cloth a special status which has helped to sustain its popularity as an object of veneration.
"What counts the most is that this shroud, as you have seen, reflects in a clear and precise manner how the gospels describe the passion and death of Jesus," said Cesare Nosiglia, the archbishop of Turin.
"It is not a profession of faith because it is not an object of faith, nor of devotion, but it can help faith."
Piero Fassino, the mayor of the city best-known as the home of carmaker FIAT and Juventus football club, said the shroud was woven into the city's identity.
"Hundreds of thousands of pilgrims will come to our city over the course of 67 days," he said. "We will welcome them with open arms."
The shroud's enduring appeal is set to be underlined by the huge numbers of pilgrims and other visitors expected in the northern Italian city between Sunday afternoon and June 24th, when it will be exhibited for 12 hours a day (0730-1930) in the Cathedral of St John the Baptist.
Slots to view the shroud are free but have to be reserved via the website www.sindone.org or a special call centre. As of Saturday more than one million had been booked with several days already blocked out.
Viewers will be afforded only a few minutes each in front of the original although they will be able to linger longer in front of a specially-made model and a related exhibition.
When the shroud was last presented to the public, in 2010, more than two million people filed past it.
Pope Francis decreed the latest exhibition to mark the 200th anniversary of the birth of St John Bosco, a 19th Century monk who devoted his life to the education of poor children in newly-industrialized Turin. Francis, who has family roots in the region, is due to visit the city and the exhibition on June 20th-21st.