The embassy is to remain closed on Monday so that it can be disinfected, the ministry said, adding that authorities in Greece and Israel are in close contact over the matter.
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The Health Ministry later confirmed that the worker and their family are Israeli nationals.
The ministry said he was on the following flights and urged anyone who was also on those flights to enter self-quarantine: El Al flight 542 from Athens to Tel Aviv on March 1 at 10:40 a.m., El Al flight 71 from Tel Aviv to Mumbai on March 1 at 8:15 p.m., El Al flight 72 from Mumbai to Tel Aviv on March 5 at 10:50 p.m., and Aegean flight 922 from Tel Aviv to Athens on March 6 at 5:40 a.m.
The near-empty departure halls of Ben Gurion Airport on March 8, 2020. (Flash90)
The worker is not the first person found to have been infected after being in close proximity to the group of Greek travelers. The condition of the 38-year-old bus driver from East Jerusalem who drove them has deteriorated and he is unconscious and breathing with a respirator, the hospital said Sunday.
Fourteen Israelis were added Sunday evening to the list of those who have contracted the coronavirus, including the first in the country whose source of infection was unknown, bringing the total number of cases to 39. Seven of the new patients returned from European countries, and six came into contact with sick individuals in Israel.
Also on Sunday evening, Prime Minister Benjamin Netanyahu said at a press conference that if Israel decides to expand the list of countries from which returning travelers will be required to enter home quarantine for 14 days, the directive will cover the entire world, adding that a decision on the matter would be made in the coming hours.
Despite the expectation that Netanyahu would announce a directive against passengers returning from the US, or at least particular states where the highest number of cases have been documented, he avoided doing so.
Prime Minister Benjamin Netanyahu (L) and Health Minister Yaakov Litzman during a press conference about the coronavirus at the Prime Ministers Office in Jerusalem on March 8, 2020.
Health Ministry deputy director general Itamar Grotto on Sunday estimated that the number of Israeli COVID-19 cases could surge to tens of thousands.
Netanyahu declared on Saturday that the disease was a pandemic.
The virus hit a milestone Friday, infecting more than 100,000 people worldwide. It has killed nearly 3,400 people.
Israel has already required returning Israelis from several countries to self-quarantine, and barred foreigners from a slew of European and Asian countries. Some 80,000 Israelis are now reported to be in self-quarantine, and large events such as concerts and sporting matches have been canceled.
Israelis have also been advised against all non-vital international travel.