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A spike of coronavirus cases in Mexico City is raising concerns that the jam-packed capital of some 20 million people living in close quarters could be the world’s next hot spot.

In the city, there are more than 7,500 positive cases and more than 600 deaths — about a quarter of the national total — though health authorities suspect the real number of infections is much higher. People are falling sick, dying, and being cremated often before families receive test results, if they come at all.

A hospital worker calls out a name from the gate, as relatives of hospitalized patients wait outside in hopes of receiving news of their loved ones, at a public hospital in the Iztapalapa district of Mexico City, Tuesday, May 5, 2020.  (AP)

"We have to prepare ourselves for the hardest, ugliest part," said Dr. Mauricio Rodríguez of Mexico's National Autonomous University. “There will be more hospitals filled to capacity and more deaths.”

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Critics have accused Mexican President Andrés Manuel López Obrador of compounding the problem with his mixed messages and lax enforcement of social distancing.

In the early days of the outbreak, López Obrador refused to implement sweeping lockdown measures in Mexico and claimed that his rivals would see him in self-isolation as a time to overpower him politically and take control of the government.

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Meanwhile, Mexico has extremely limited testing compared to other countries, which makes experts believe the country's infections are much higher. Mexico City Mayor Claudia Sheinbaum said recently the city was performing only about 700 tests per day. The government has defended its limited testing of only people meeting a list of criteria, but it has left a growing number of families unsure of what killed their loved ones.

Fox News' Lucia Suarez and The Associated Press contributed to this report.