(CNN) Nine Texas mayors, including those in Houston, Dallas, Austin and San Antonio, have urged Gov. Greg Abbott to give them the authority to require masks be worn in public "where physical distancing cannot be practiced."
In a letter to Abbott, the mayors said "many people in many of our cities are still refusing to wear these face coverings even though these coverings are scientifically proven to help prevent the disease from spreading."
A growing number of studies show face masks reduce the spread of the coronavirus, especially because many people are contagious before they have symptoms and because this virus can spread easily by just talking or breathing. But some people have refused to wear masks, claiming it infringes upon their civil liberties.
Abbott, a Republican who has repeatedly said masks are important, has insisted that government should not force people to wear masks. His executive order to reopen the state expressly banned local jurisdictions from doing so.
In a surprising move Wednesday, Bexar County -- home of San Antonio -- issued an order mandating businesses to require face coverings for employees and visitors when they could be in close proximity. Those who don't face a fine of up to $1,000.
The order puts the burden on businesses to enforce wearing face masks in their facilities. But it's still the county that would impose the fine if businesses don't follow suit.
Perhaps more surprisingly, Abbott said he supports Bexar County's new requirement, noting his statewide order bans local government from requiring masks for individuals -- but doesn't ban businesses from requiring masks in their own facilities.
"We want to make sure that individual liberty is not infringed upon by government and hence government cannot require individuals to wear a mask," Abbott told CNN affiliate KWTX.
"However, pursuant to my plan, local governments can require stores and businesses to require masks. That's what was authorized in my plan, that's what the Bexar County judge has now realized. And so what Bexar County is doing and what every county is authorized to do, and that is to impose requirements on business operations."
Other parts of Texas could enact similar rules. Dallas County Judge Clay Jenkins, the head of the county government, said he was glad the governor supported Bexar County's mask rules.
"Once enacted in Dallas County and in other local jurisdictions, this will save countless lives," Jenkins said.
This week, 10 states are seeing their highest seven-day average of new coronavirus cases per day since the pandemic started months ago, according to a CNN analysis of data from Johns Hopkins University.
The data includes new cases reported through Tuesday. The states seeing record-high averages are Alabama, Arizona, California, Florida, Nevada, North Carolina, Oklahoma, Oregon, South Carolina and Texas.
While some politicians have attributed higher case numbers to better testing, recent surges are outpacing the increase in tests, said Dr. Ezekiel Emanuel, chair of the Department of Medical Ethics and Health Policy at the University of Pennsylvania.
"You can have a small percentage increase because of testing in terms of number of cases," he said.
"But when you see 50% or 150% increase in the number of cases you are seeing -- which is what we are seeing across the South -- that's not testing. That's new cases. That's community spread."
An estimated 230,000 to 450,000 Covid-19 cases were prevented in the states that enacted requirements for mask use between April 8 and May 15, researchers from the University of Iowa reported Tuesday.
The longer the rules were in place, the higher the reduction in Covid-19 cases. Within a week after implementation, for example, researchers observed a 0.9% decline in new Covid-19 cases. After 21 days, they reported up to a 2% decrease.
Another study published in the Lancet medical journal also said wearing a face mask decreases the chances of spreading coronavirus.
But many people are skipping face masks as states reopen. That's the opposite of what needs to happen, since many more people are out in public, said Jeremy Howard, a research scientist at the University of San Francisco.
Howard has spent the past four months in Texas and has noticed fewer people wearing masks recently.
"As economies open up more, masks become more important -- not less important," he said.