Benjamin Todd Jealous, the president of the National Association for the Advancement of Colored People, praised the decision, saying the state law “would have blocked hundreds of thousands of Hispanic voters from the polls just because they lack a state-issued photo ID.”

But Gov. Rick Perry called the decision “yet another example of the Obama administration’s continuing and pervasive federal overreach.” He argued that there was “no valid reason” for rejecting the law since it required “nothing more extensive than the type of photo identification necessary to receive a library card or board an airplane.”

Under the state’s existing system, voters are issued certificates when they register that enable them to vote. But last year, Mr. Perry signed a law that would replace that system with one requiring voters to present one of several photographic cards at their polling station.

The approved documents include a state-issued driver’s license or identification, a license to carry a concealed gun, or several forms of federal identification. Student identification cards would not count.

The measure was part of a wave of new voting restrictions passed around the country, mostly by Republicans, after their sweeping victories in the 2010 elections. More than a dozen states tightened election rules, including eight that passed variations of a photo identification rule.

Supporters argue that such restrictions are necessary to prevent fraud. In a statement, Greg Abbott, the Texas attorney general, said state prosecutors had won about 50 convictions related to various kinds of election fraud over the past decade, and he listed several that appeared to involve in-person voter impersonation — the kind addressed by photo ID requirements.

Critics say there is no evidence of significant amounts of in-person voter impersonation fraud and contend the restrictions are a veiled effort to suppress turnout by legitimate voters who tend to vote for Democrats, including students, the indigent and minorities.