Texas Gov. Greg Abbott told "Hannity" Tuesday that he did not want to shut down his state again, even as the number of new coronavirus cases and total hospitalizations hit a new high in the Lone Star State.

"Sean, know this," the Republican told host Sean Hannity. "We do not want to shut down business or Texas again. We cannot have that. What we can do, however, we can use these practices ... people can wear masks. We can use these other strategies to slow the spread while we are awaiting the time when we do have these vaccines."

Abbott also assured viewers that "we will have therapeutic drugs coming in maybe two or three months before vaccines will come, so that people will be able to be treated who do contract COVID-19."

Earlier Tuesday, The Texas Department of State Health Services reported 10,745 new coronavirus cases and 10,569 total coronavirus hospitalizations, new highs in both categories. Also Tuesday, the seven-day rolling positive test rate average reached a new high of 16.89 percent, up from a low for 4.27 percent May 26.

"We're seeing two things," Abbot said. "One is, we are seeing a meaningful increase in hospitalizations, and that is a very dangerous sign. We are seeing, however ... almost half of the people who are testing positive are under the age of 35.

"As a result, it means that more of the people who are testing positive will not be going to hospitals as before. But we do need to be very concerned about those who are hospitalized. But also, we must emphasize ... the young adults who do test positive, they can spread that with their parents, with their grandparents, and that can lead to the serious problem."

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Abbott concluded his interview by calling on Americans to wear masks to combat the virus.

"It's so important that people in Texas, as elsewhere, wear a mask ..." he said. "This isn't just Texas and Florida. Remember ... what's going on in California and Louisiana, in Illinois, all of which have upticks in the number of cases.

"My point is this," the governor went on. "The coronavirus, COVID, is not blue. It's not red. It's not Democrat. Not Republican. It's going to happen in any state. And we all just need to respond in ways to contain it without crushing our economies and without killing jobs."