AUSTIN, Texas — Gov. Greg Abbott is striking an urgent tone in telling Texans to continue taking precautionary measures to slow the spread of COVID-19. But he stopped short of pulling back on any of his phased re-openings amid rising cases and hospitalizations.

In a press conference Monday, Abbott said, in the past five days Texas averaged more than 3,500 cases a day. The COVID-19 positivity rate -- or the ratio of confirmed cases to tests -- has gone from about 4.5 percent in late May to almost 9 percent as of June 22. In the last five days, hospitalizations have averaged more than 3,200 a day.

"To state the obvious, COVID-19 is now spreading at an unacceptable rate in Texas, and it must be corralled. We have several strategies to reduce the spread without having to shut Texas back down," Abbott said.

Abbott didn't offer any new policies. Instead, he emphasized voluntary guidelines that have been consistently pushed like wearing a mask, staying home if you can, sanitizing your hands and keeping six feet apart.

"I know that some people feel that wearing a mask is inconvenient or that is like the infringement of freedom, but I also know that wearing a mask will help us to keep Texas open," Abbott said. “Not taking action to slow the spread will cause COVID to spread even worse, risking people's lives and ultimately leading to the closure of more businesses."

Abbott did say Texas hospitals do have an abundance of beds and the state succeeded in the early goal of preventing hospitals from being overrun. He also said the state was working with hospitals to ensure they have capacity, surging testing in potential hot spot areas and stepping up enforcement of places like bars where large crowds have gathered.

"The way that hospitalizations are spiking, the way that daily new cases are spiking, surely the public can understand that if those spikes continue, additional measures are going to be necessary to make sure we maintain the health and safety of Texans," Abbott said.

He said closing Texas again will be the last option. But a coronavirus expert argued the state should be pulling back now.

“I think it’s pretty clear that what we’re doing isn’t working very well right now and when you’re doing something that’s not working, the best idea is to change in some way,” said Dr. Benjamin Neuman, professor and chair of the biological science program at Texas A&M University-Texarkana.

Dr. Neuman said a statewide mask mandate would be a good step to take.

Click the video link above to watch our full interview with Dr. Neuman.