TEHRAN—Iran closed schools and imposed emergency measures in a central province near the country’s capital after two people who tested positive for the coronavirus died, the first fatalities in the Middle East from the disease.

Five people so far have been diagnosed with the Covid-19 virus, Iran’s health ministry said Thursday. Four of them in the city of Qom, one of the country’s main pilgrimage sites about 75 miles south of Tehran, where the two elderly patients died a day earlier.

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