Editor's note: This story has been updated with statements from Harris County Judge Lina Hidalgo, Houston Mayor Sylvester Turner and Houston Police Chief Art Acevedo.

Gov. Greg Abbott said Monday that local officials cannot impose penalties on residents who violate rules about wearing masks in public — including those in Harris County, where county Judge Lina Hidalgo’s mask order went into effect that morning.

“We strongly recommend that everyone wear a mask,” Abbott said at a press conference where he announced his plans for reopening Texas. “However, it's not a mandate. And we make clear that no jurisdiction can impose any type of penalty or fine.

“My executive order, it supersedes local orders, with regard to any type of fine or penalty for anyone not wearing a mask,” he added.

Hidalgo’s order, which carries a penalty of up to $1,000, drew harsh criticism from GOP officials and members of law enforcement. The measure is similar to those ordered by other local officials, such as those in Austin and Dallas.

Asked about Abbott's order superseding her own, Hidalgo said, "In practical terms, the governor’s order doesn’t change much because, like every order we’ve issued so far, we’d made it clear that the priority was education.

"We have a face covering order today, and we’ll still have a face covering order tomorrow," Hidalgo said in a statement. "The fine was there as a signal of how vital mask wearing is, and in many ways, the community got that message. It’s been disappointing to see folks politicize public health, and I hope this means they'll go back to focusing on health and safety instead of politics. As we have in the past, we will amend this order to conform with the governor’s."

At a news conference shortly after Abbott’s announcement, Houston Mayor Sylvester Turner said residents will still be told to wear masks, though police won’t issue tickets for violations.

"If you run into someone in a uniform ... he's not going to give you a ticket, he'll offer you a mask," Turner said. "That's what we're emphasizing, because it's all about your health."

Chief Art Acevedo of the Houston Police Department warned residents that businesses can still require customers to wear masks.

"If they ask you to wear a mask, you must wear a mask, and if you fail to leave the premises, you are subject to a criminal trespass warning or a criminal trespass arrest," Acevedo said Monday afternoon at the press conference.