WASHINGTON—A three-judge panel rejected Texas' voter-identification law, saying it violates civil-rights protections by putting an unfair burden on poor and minority voters, in a ruling that adds to a legal fight between the parties heading into the presidential election.

It is the second loss for Texas this week on a significant election-law issue. Earlier, a three-judge panel concluded the state had improperly redrawn its voting districts to the disadvantage of minority voters.

...