The news comes as Texas hit a second daily record of over 10,000 cases on Saturday.
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As of Sunday, Texas has a total of 258,659 total cases, with 3,192 deaths reported. Harris County leads the other counties with a 43,939 total.
According to Harris County Public Health, only 97 ICU beds were available on Sunday because of the overwhelming demand.
READ MORE: Texas shatters daily record with 10,351 new coronavirus cases
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Previously, the federal government had announced they were withdrawing support from Harris County and Houston's large stadium-based test sites. But, in June, Abbott announced that federal funding had been secured to extend community-based test sites in Texas.
"These federally-supported testing sites are a vital component," said Abbott. "I thank our federal partners for extending these operations in Texas, and for their flexibility in allocating their resources to the communities of Dallas and Houston that are experiencing a high number of COVID-19 cases right now."
Harris County and Houston-area testing sites can be found on their websites.