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A Texas mayor has criticized the state's face mask requirement, telling Fox News Tuesday that elected officials should call on people’s “higher nature instead of trying to exercise the authority we don’t have that is remaining unchecked in many municipalities and states.”

“People are trying to do the right thing, and the fact of the matter is, whether we have a law in place or not, people are going to continue to do what they are trying to do,” Midland Mayor Patrick Payton told “America’s Newsroom."

Payton added that“authority needs to be checked before it runs rampant and we become comfortable in being overrun in our civil liberties.”

Last week, Texas Gov. Greg Abbott mandated the wearing of face coverings in public in all Texas counties with 20 or more confirmed COVID-19 cases, following record increases in infections in the state.

“It's really not a message of no face mask," Payton told Sandra Smith Tuesday. "It’s a message of how you communicate that and how you enforce that quite simply.

“Throughout Midland we have been encouraging people and encouraging businesses and people all over the city to wear face masks, to do the things that we are being asked to do to protect public health,” he continued. “When we have a breakdown is when we mandate things and we are called upon to enforce things.”

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“We’re asking our people to do exactly what they did in March, which is do the right things to flatten the curve and they did exactly that," Payton went on.

“We’re asking them to do that now, but we’re not going to send our police department out when they have a job to do already and we’re already understaffed as a police department in this region."

In that vein, Payton said, police officers “will not be answering 911 calls because someone saw someone walking five feet apart instead of six feet apart without a face mask or they saw someone at the grocery store without a face mask.”

“It's not an anti-face mask message," he emphasized. "It's an anti-overreach message is what it is."

The mayor told Smith that he "absolutely" wears a face mask in response to an inquiry by Smith.

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“A free people who are self-governing can do these best practices and protect themselves and the people around them without a mandate being handed down," he added, "and that's what we are doing here in Midland, Texas."

Texas has reported more than 200,000 coronavirus cases and 2,655 deaths as of Monday, according to the Texas Department of State Health Services.

Fox News' Morgan Phillips contributed to this report.