Italian Health Minister Roberto Speranza said on Friday people who have been in Romania and Bulgaria in the past 14 days will be quarantined upon arrival in Italy, a move aimed at preventing the importation of Covid-19 cases.
"We found out with great bitterness the decision of the world number two to cancel her participation," the tournament's director Oliviero Palma said in a statement.
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He said the organisers had written an urgent letter to Italy's health minister, asking for exemption for tennis players taking part in the event.
"Yesterday we were optimistic, and we had informed Halep's staff about the fact that professional players are not obliged to quarantine," Palma said, adding that the Romanian's team only responded to tell him that she was withdrawing. "We are embittered and profoundly disappointed."
Palermo will have strict health precautions and all players will undergo Covid-19 tests before they attend, on arrival and every four days subsequently, as it will be the first professional tennis event across either tour after a five-month break, with action scheduled to get underway on the clay courts of the Sicilian capital from August 3.

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Halep responded with a brief statement on social media.
"Given the recent rise in Covid-19 cases in Romania and my anxieties around international air travel at this time, I have made the tough decision to withdraw from Palermo," she wrote on Twitter.
"I want to thank the tournament director and the Italian ministry of health for all their efforts on my behalf and I wish the tournament a successful week."
Halep had confirmed her entry to Palermo only a fortnight ago, releasing a video in which she said: "I'm very happy to announce I will be back in Palermo after ten years. Hope to have a great week over there."
Halep, the reigning Wimbledon champion and 2018 French Open winner, has also committed to the Prague Open, scheduled to start on August 10.
Italy was the first European country to be hit hard by the novel coronavirus but the amount of daily new infections being reported is a fraction of the numbers in late March. The country has recorded over 35,000 deaths from the virus.
Players still committed to Palermo include British number one Johanna Konta, French Open finalist Marketa Vondrousova, and top-ranked Italian Camila Giorgi.
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