During a briefing on Monday, the governor announced infection rates have gone from 4.5 percent in May to 9 percent.
"Hospitalizations for COVID-19 average just over 1,600 a day in the latter part of May," explained the governor. "In the last four or 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."
However, Abbott said there is now more testing being conducted in hot spots across the state, and said they're working with hospitals to make sure anyone with COVID-19 receives the proper treatment.
"Closing down Texas again will always be the last option," said Abbott.
Abbott continues to push for Texans to stay at home, wash their hands and practice safe social distancing.
WATCH: Would Gov. Abbott consider scaling back on his reopening plan?
As the fight to bring down the number of cases continues, last week, seeking to explain the trend, Abbott pointed to temporary spikes in positive tests in some isolated areas. But he also suggested young people specifically are not taking the virus seriously enough, saying there are "certain counties where a majority of the people who are testing positive ... are under the age of 30, and this typically results from people going to bar-type settings."
SEE ALSO: Gov. Abbott suggests Texans under 30 ignored virus warning signs
Multiple big-city mayors have asked Abbott to grant them the "authority to set rules and regulations" mandating face masks during the coronavirus pandemic.
The plea to grant rules and regulations was made due to an executive order from Abbott that bans local governments from imposing fines or criminal penalties on people who don't wear masks in public.
SEE ALSO: Texas' big-city mayors ask Gov. Greg Abbott for power to impose face mask rules
A letter signed by various mayors, including Houston's Sylvester Turner, asks Abbott to consider allowing each city's local officials to decide whether to require the use of a face covering in order to prevent the spread of the virus.
Since then, various cities and counties have issued their own mask orders, which mandates businesses require employees and customers to wear face coverings. Failure to comply, businesses could face up to $1,000 in fines.
In Harris County, the mask order goes into effect Monday, June 22.
"The idea is to see this as a no shirt, no shoes, no mask, no service," Harris County Judge Lina Hidalgo said.
SEE ALSO: What to know about Harris County's new face mask order