The clinics filed an emergency motion asking the justices to overturn a lower-court order and allow abortions when they can be performed using medication.
Texas Gov. Greg Abbott issued an executive order last month that bars non-essential medical procedures so that medical resources can go to treating coronavirus patients. Texas' attorney general has said that providing abortions other than for an immediate medical emergency would violate the order.
A three-judge panel of the 5th U.S. Circuit Court of Appeals on Friday allowed abortions to proceed in cases where a woman would be beyond 22 weeks pregnant, the legal limit for abortions in Texas, on April 22, the day after the governor's order barring non-essential medical procedures is set to expire.
But the appeals court order blocked for now medication abortions, which are allowed in Texas during the first 10 weeks of pregnancy. In a medication abortion a woman takes one pill at a clinic and then takes a second pill 24 to 48 hours later, typically at home. The clinics have argued that medication abortions do not require personal protective equipment like masks, gloves and gowns that might be needed for coronavirus patients.
Similar legal fights over abortions during the pandemic are ongoing in Alabama, Ohio and Oklahoma.