The businesses have argued in court documents that Mr Abbott’s recent executive order, which paused the further reopening of the state and forced them to close, has singled them out unfairly, according to CBS News.
In mid May, Texas reopened bars with a 25 per cent capacity limit, which was increased to 50 per cent in June, as part of its reopening of the state, but has seen a dramatic rise in coronavirus cases in the last couple of weeks.
On 25 June, a day before Mr Abbott halted any further reopening of the state, Texas recorded its highest single day total of positive coronavirus tests, with 5,996 new Covid-19 cases.
The following day, the governor announced that bars and other outside businesses were to close and blamed the rise in cases on “certain types of activities, including Texans congregating in bars”.
Lawyers representing the bar owners said in court documents that Mr Abbott’s order meant their clients had been “relegated to Abbott’s loser category and sentenced to bankruptcy.”
They added that it does not make sense that other businesses, such as nail salons and barber shops, which require closer proximity between staff and customers, have still been allowed to stay open.
The lawyers argue in the lawsuit that the decision to only keep some businesses open goes against the state’s constitution, and they asked for an undefined amount of “compensatory damages”, and for a judge to ban Mr Abbott’s order temporarily.
“Governor Abbott can claim all day that the legislature gave him broad powers,” the documents read. “However, those powers that Abbott claims to have, whatever they may be, cannot supersede the Texas Constitution.”
Bar owners and employees marched in Austin on Tuesday against the order, with some chanting “bar lives matter”.
Any bar owner caught violating the governor’s order will have their alcohol licence suspended, as has happened to seven so far, according to the alcohol commission.
On 26 June, Mr Abbott said that he was only temporarily pausing the state’s easing of lockdown measures, as he felt it was important to get the virus under control and continue to move forward.
“The last thing we want to do as a state is go backwards and close down businesses,” he said.
“This temporary pause will help our state corral the spread until we can safely enter the next phase of opening our state for business.”
According to a tracking project hosted by Johns Hopkins University, there are now more than 2.6 million people who have tested positive for coronavirus in the US. The death toll has reached at least 129,544.