"As people move forward, please be mindful," said Turner. "The virus is still in our city."
Turner's appearance came after Gov. Greg Abbott announced the number of recoveries have exceeded the number of active cases in the state for the past two days.
GREAT NEWS:— Greg Abbott (@GregAbbott_TX) May 3, 2020
The number of Texans who have RECOVERED from #COVID19 now exceeds the number of active COVID cases for the past 2 days.
That’s exactly what we want to see.
Texas ranks 3rd highest among states for number of people who have recovered from #coronavirus. #txlege
Statewide on Saturday, Texas hit a third straight day of more than 1,000 new coronavirus cases. Starting May 1, residents were allowed to go back to malls, restaurants, movie theaters and retail stores in limited numbers.
However, on the first weekend of major businesses reopening in Houston, Turner said the city matched its highest single-day death total on Saturday.
He urged the public to continue to wear masks, mentioning that 25-30% of people are asymptomatic.
Council member Abbie Kamin also urged the public to fill out the U.S. Census, ensuring adequate resources would be brought back to Houston to fight things like this disease.
Regarding the governor's order that restaurants should only operate with 25% capacity, Turner said it's a self-policing matter and up to business owners to comply. The city lacks the resources to visit each establishment to check if all are following the mandate, Turner said.
The mayor reported 73 new cases of COVID-19 on Sunday, bringing the total city's count to 3,908. Four more people died due to the virus, bringing the total death count to 69.
On Saturday, the mayor reported 115 new COVID-19 cases and five new deaths.
"In this entire time period, we've never reported in the city of Houston more than five deaths, so this equals the maximum that we have ever reported of people that passed away on any given day," Turner said.
In the middle of his update, the mayor briefly spoke about the adult entertainment club that attempted to open Friday night, but was shut down.
RELATED: Federal judge allows Houston strip club to open as restaurant
"We have been attempting to enforce the governor's order that he put out. There was a strip club that wanted to characterize itself as a restaurant. We closed them down on Friday," Turner said.
He also asked for the governor to clarify his order for businesses like strip clubs that intend to open too soon.
"It is important for the governor to clarify his order for the businesses that are starting up and inform them that he did not intend to include strip clubs in those businesses. Then the state attorney general needs to aggressively enforce his order. Otherwise, it opens the door for more and more people to attend these businesses," Turner said.