Although the governor issued an executive order June 3 banning local governments from imposing fines or criminal penalties on people who don't wear masks in public, Abbott on Wednesday commended Wolff for putting the onus for face masks on businesses. In an interview with KWTX, Abbott said the local official "finally figured that out."

"Government cannot require individuals to wear masks," he added. "Local governments can require stores and business to require masks. That’s what was authorized in my plan."

But those assertions have brought quick criticism from local officials — and lawmakers from within Abbott's own party.

City and county officials, some of whom signed on to a letter asking for the power to mandate face masks, fault Abbott for two things. They say he should have explicitly told them that businesses could require face masks. And, they say, his lack of a statewide mandate even as he emphasized the importance of wearing a mask prompted some Texans to let their guards down against taking precautions to stop the virus' spread.

A spokesman for the governor did not immediately respond to a request for comment Friday.

Abbott's comments about Wolff figuring out what the governor's order allows came the same week that Texas continuously set new records for coronavirus infections and hospitalizations. More than 3,100 Texans were hospitalized with COVID-19 on Friday, the eighth day in a row that a new record for hospitalizations was set. And the state reported more than 3,000 new infections a day three times this week, after previously never exceeding that threshold. Those infections and hospitalizations come several weeks after Abbott allowed businesses to begin reopening.

"Our best tool for fighting this pandemic is public trust, and the work that we have to do and putting the public health guidance out front, so that people have the information that they need to make good decisions for their businesses, for themselves and their families is critical," San Antonio Mayor Ron Nirenberg said Friday. "When the orders at any level of government are so obtuse that our partners can't figure them out, it's not to be celebrated."

As of Friday, Bexar, Travis, Hidalgo, Cameron, El Paso, Harris and Dallas counties have issued orders mandating businesses require face masks or risk fines up to $1,000. Hays County officials' order does not impose a fine on non-compliant businesses.

Tarrant County Judge Glen Whitley said he does not plan on issuing an order.

"While we all agree that we’re glad the governor has given us that authority, we do not feel like at this point in time, at least in Tarrant County, that we want to require it," Whitley said Wednesday, the Fort Worth Star-Telegram reported.

State Rep. Erin Zwiener believes the reason Abbott allowed for Bexar's order to go through is because of the rising number in coronavirus cases and hospitalizations. She said she doubts state officials would have allowed the order a month ago.

"Either the attorney general would have ruled it didn't line up with his order or Governor Abbott would have adjusted his order to get rid of that loophole," she said.

Abbott initially appeared largely amenable to cities and counties interpreting his earlier directives however they saw fit, deciding when to arrest or fine violators, warn them verbally, leave informational flyers or do nothing at all. Then, he changed his mind and, along with the state’s other Republican leaders, blasted local officials in Dallas and Houston for what they called overzealous enforcement of COVID-19 regulations.

"Ideas were being discussed, people were looking for loopholes, the issue is that the governor created a situation where locals felt like they had to be cautious to avoid being cracked down upon," Zwiener said. "We wasted the benefit we got from our shut down by not having well-established practices in our businesses that they opened, and not clearly communicating to the Texas public the behavioral modifications they needed to make."

At an April press conference where he talked about plans for reopening the state, Abbott took away local officials' ability to issue fines for violating coronavirus-related orders, adding that his executive order "supersedes local orders, with regard to any type of fine or penalty for anyone not wearing a mask."

Meanwhile, the governor is taking heat from fellow Republicans for not opposing the Bexar order.

In his Capitol Report newsletter Friday, state Sen. Bob Hall, R-Edgewood, criticized the way the orders are now placing the enforcement responsibility on business owners, saying it is "bizarre, convoluted, and confusing."

"Business owners will become a de-facto law enforcement arm, but the only tool they will have to enforce the mask requirement is to refuse to sell to their customers and to kick them out of their store," Hall wrote. "These are the same businesses that the Governor recently declared non-essential and ordered shut down for months."

State Reps. Kyle Biedermann, R-Fredericksburg, Tony Tinderholt, R-Arlington, Jonathan Stickland, R-Bedford, and Mike Lang, R-Granbury, also denounced Abbott in a Thursday letter, telling him to "stop playing games."

"It is inconsistent to say you believe Texans should be free to make their own decision on whether to wear a mask or not but use the heavy hand of the government to punish business and make them enforcers of tyranny on freedom loving Texans," they wrote.

Meanwhile, El Paso Mayor Dee Margo, a former Republican lawmaker, said he does not think the counties' face mask orders are an "onerous burden," but a small price to pay to keep the economy open and stop the spread of the virus.

"We're going to have to figure out how to live with this virus and do the things that need to be done in order to stop the spread and keep our economy open to the extent that we can do it in a safe manner," he said.

The Texas Tribune is a nonpartisan, nonprofit media organization that informs Texans — and engages with them – about public policy, politics, government and statewide issues.