"This virus is still very much alive and still present within our community," Turner said.
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While volunteering at a food distribution drive in northwest Houston, Turner announced 183 new COVID-19 cases in Houston, bringing the total to over 6,500.
He said of those 183 new cases, 77 were from homeless shelters.
"We are now testing people in our homeless shelter, and what we are finding is there are people who are infected with this virus. We are engaging in social distancing and spreading them out," Turner added.
He also announced one new death of a woman in her 60s who had no underlying medical conditions. The city's death total is now 125.
Turner added that of those 125 deaths, 27 came from nursing homes, and three came from the Harris County Jail.
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Turner also addressed the first night of bars reopening after a more than 30-day closure due to the pandemic.
"We have to remind people that this virus has not disappeared. This is one of those times as things start to open back up, people are going to have to police themselves," Turner said.
He said he's encouraging businesses to adhere to Gov. Greg Abbott's orders, and not exceeding the 25 percent capacity limit.
Turner also said the city of Houston, along with the health department, will open two more testing sites.
"That's the thing, with more testing we anticipate more positive cases. That's not a bad thing, because it's important for people to know whether or not they are infected with the virus so they don't continue to spread it to other people," Turner said.