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\"We have to face reality: managing this crisis goes way beyond knowing how many hospital beds are available,\" state Rep. Chris Turner, chairman of the Texas House Democratic Caucus, said in a statement. \"Our state's positivity rates are too high and still increasing, and positive cases and hospitalizations continue to rise. And we still have yet to reach the daily testing goals Gov. Abbott set forth nearly two months ago.\"

State Rep. Erin Zwiener, whose district includes Hays County, also said Abbott's comments included \"several inaccuracies that minimize the severity of the situation\" in the county.

\"New hospitalizations and the testing positivity rate are also increasing, and Hays County reported that they were behind on paperwork due to high case counts,\" Zwiener said in a statement. \"Case counts in Hays County have increased more than 5 fold in a week.\"

On Tuesday evening, a bipartisan group of mayors in nine Texas cities also sent Abbott a letter urging him to grant them the authority to require face masks as the number of cases goes up.

\"With the increase in testing, we are naturally seeing more people being diagnosed with COVID-19, and some areas are seeing confirmed cases increasing more rapidly than testing,\" the letter said. \"While it's important to get our economy working again, we must also take precautions to avoid a massive influx of new cases overwhelming our hospitals.\"

The letter noted that masks \"could prove to be the most effective way to prevent the transmission of this disease,\" yet many people in their cities are not wearing them.

.@HouMayor Turner joins \"Big City\" #Texas mayors in urging Gov. Abbott to allow local control on #FaceMasks to protect citizens from #COVID19 spread. Read more here https://t.co/S4XJvJHMs9 pic.twitter.com/SE6IKtORld

— City of Houston (@HoustonTX) June 16, 2020

\"A one-size-fits-all approach is not the best option. We should trust local officials to make informed choices about health policy. And if mayors are given the opportunity to require face coverings, we believe our cities will be ready to help reduce the spread of this disease,\" the letter said.

In response to the letter, Abbott spokesman John Wittman told ABC News, \"None of these local officials have lifted a finger to impose penalties and enforcement mechanisms currently available to them. The one time a county judge did, a business owner wound up in jail.\"

ABC News' Ali Dukakis and Leah Larosa contributed to this report.

What to know about the coronavirus:

Tune into ABC at 1 p.m. ET and ABC News Live at 4 p.m. ET every weekday for special coverage of the novel coronavirus with the full ABC News team, including the latest news, context and analysis.

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