The 987 new coronavirus cases brought Houston's total to 16,253 cases.
Turner also announced seven more deaths, bringing the city's total to 204. Among the deaths, 57 were associated with nursing homes and three were from the Harris County jail, Turner added.
"The numbers are moving in the wrong direction, but we are asking people to do what we did early on and take this thing very seriously," Turner said during a briefing that also included the formation of a new policing reform task force.
In the midst of a clear upward trend involving cases and hospitalizations, Turner pleaded with the federal government over FEMA-backed testing sites in Houston, which he said will close on June 30.
More than 60,000 people received free testing at the sites, Turner said.
Turner also promised to announce instructions to police and fire departments to monitor business, clubs and bars, especially with the weekend ahead. He called for a crackdown on mask and occupancy violations, going as far as proposing a "board of shame" to identify non-compliant businesses.
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