He was joined by Dr. David Persse and Houston Fire Department Chief Sam Pena.
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He announced there were 1,544 new cases bringing the total to 30,065 cases. Of the total cases, 73 are associated with nursing homes and three are associated with the Harris County Jail. There are eight new deaths bringing the total to 277.
Turner mentioned Houston Rockets star Russell Westbrook tested positive for the virus.
"This virus does not care who you are," said Turner.
SEE RELATED STORY: Houston Rockets star Russell Westbrook has COVID-19
He announced the medical task force arrived Monday and is looking at establishing a wing at United Memorial Medical Center.
There will be patients transferred from other hospitals.
Dr. Persse also said a third medical resort is being looked at opening at a closed nursing home in the Willowbrook area.
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Over the weekend, Turner said he proposed to Gov. Greg Abbott a two-week shutdown to "re-calibrate" as cases of the virus continue to increase.
SEE RELATED STORY: Mayor Sylvester Turner proposes 2-week shutdown to 're-calibrate'
While Turner has not spoken to Gov. Abbott about the two-week shutdown proposal, he said he is aware of the request.
He said there is a focus on slowing down the virus this month to help in the efforts of sending kids back to school in the Fall.
Dr. Persse announced the positivity rate increased from 25.2% last week to 26.8% this week. It was at 14% in the month of March.
"Don't go to big parties," said Persse. "Just follow the rules. It's not that hard."
Pena said no fire stations are closed, however staffing is strained. There are 190 firefighters that remain in quarantine.
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"We can all do our part to limit our exposure to first responders," he said.
The department has received 50 complaints in the last 24 hours, but none of those complaints were forwarded to TABC, according to Chief Pena.
Turner said Saturday he believes there's nothing wrong with taking a few steps back and he acknowledged the city reopened too quickly.
"We have to acknowledge the fact that the numbers are continuing to rise," said Turner. "Not everybody is going to wear a mask. Let's be real. Even with the requirement."
SEE RELATED STORY: Gov. Abbott warns of 'lockdown' coming next if virus spread doesn't slow