03/28/2014 12:57 EDT | Updated 05/27/2014 05:59 EDT

Critics vow to keep fighting after US appeals court upholds Texas' abortion restrictions

AUSTIN, Texas - A federal appeals court has upheld Texas' tough new restrictions on abortion, meaning Dr. Lester Minto's clinic near the Mexican border will stay closed.

But Minto, who has been providing abortions for three decades, insists he'll keep helping women who call his shuttered clinic.

His is among at least 19 clinics that have closed statewide because of a new law that includes some of the nation's strictest limitations on abortion.

The 5th U.S. Circuit Court of Appeals upheld those restrictions Thursday, overturning a lower court that ruled parts of the law were unconstitutional and served no medical purpose. The appeals court said the law "on its face" doesn't impose undue burden on a woman's life or health.

The case is likely to end up at the U.S. Supreme Court.