A man wears a respiratory mask after deaths and new confirmed cases revealed from the coronavirus in Qom, Iran on February 25, 2020.

Iran's Deputy Health Minister Iraj Harirchi looked visibly feverish as he spoke on state television Monday, downplaying the spread of the new coronavirus in Iran. Without a face mask on, wiping sweat off his forehead and speaking to local press, he coughed into a tissue several times. One day later, he tested positive for the coronavirus.

Iran's health ministry has rejected claims from some local officials that the number of dead and infected is far higher than reported. Iran's government confirmed 139 cases and 19 deaths from the fast-spreading virus as of Wednesday, the highest number of fatalities outside China, where the disease has taken more than 2,600 lives and sickened more than 80,000.

"The high number of deaths in Iran suggests that the number of infections in the country is much higher than declared by the authorities," Hasnain Malik, Dubai-based managing director for frontier markets equity strategy at Tellimer, told CNBC.

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U.S. Secretary of State Mike Pompeo expressed concern on Tuesday that Tehran may be withholding "vital details" and urged all countries to "tell the truth about the coronavirus."

It's still unclear where the first cases of the virus in Iran came from; Iranian Health Minister Saeed Namaki said the first patients had previously done business in China. Another health official said it stemmed from a group of 700 Chinese clerical students studying in the religious city of Qom, where most of the cases are concentrated.

Iran hasn't suspended flights from China — one of its top trading partners — despite nearly all of its Middle Eastern neighbors doing so.

The country has canceled sports matches, concerts, and closed schools and universities in certain provinces, while workers have been disinfecting public transport venues and posting signs warning against touching surfaces in crowded places. Still, no city-wide quarantines have come into place and religious pilgrims are still moving in and out of Qom, Iran's coronavirus epicenter, which sees some 22 million religious tourists annually.