ATHENS, July 29 (Reuters) - Greece"s south Aegean islands were marked dark red on the European Centre for Disease Prevention and Control"s COVID-19 map on Thursday after a rise in infections, meaning all but essential travel to and from the region is discouraged. The cluster of 13 islands includes Greece"s most popular destinations for foreign tourists - Mykonos, Santorini and Rhodes - which, combined, draw millions of people every summer. Greek Deputy Civil Protection Minister Nikos Hardalias said later on Thursday Mykonos and Ios, another popular tourist destination, were "one step" away from authorities imposing restrictions. He said the situation was also worrying on the islands of Zakynthos, Tinos, Lefkada, Santorini, Paros and Rhodes. Greece, which depends heavily on tourism, had relied on promoting "COVID-free" islands to draw visitors back this summer, hoping a rebound in international travel would resuscitate the sector after its worst year in decades in 2020. Despite a strong June in terms of arrivals and expressions of optimism from ministers and tourism officials, uncertainty remains over how the season will unfold. read more "We"re waiting to see how the (tourist) markets will react," said Manolis Markopoulos, president of the hoteliers association of Rhodes, referring to the decision of the ECDC, an agency of the European Union. More than 90% of tourists to the island are from abroad. Germany, which this month listed Greece as a coronavirus risk area, and Britain, which has Greece on its "amber" list of countries requiring returning travellers to quarantine at home, are usually the biggest sources of visitors to Greece. The dark red zones on the ECDC map help distinguish very high-risk areas and also help EU member states uphold rules requiring testing on departure and quarantine upon return. Last week the ECDC downgraded Crete, Greece"s biggest island and another popular destination, to the dark red zone.