But the Justice Department under President Trump and Attorney General Jeff Sessions told a judge on Monday that it was withdrawing its claim that Texas enacted the law with a discriminatory intent.

The Justice Department remains a party in the case. But it is pulling back at a crucial phase. If a judge finds the state acted with discriminatory intent, as the Justice Department and other plaintiffs have alleged, Texas could be forced to seek federal approval before it makes any changes to its voting laws or procedures. That would have major impacts on voting rules in Texas and be a potent symbol of the ability of the federal government to be a major brake on voting discrimination nationally.

“This is a complete 180-degree turn,” said Danielle Lang, a lawyer for the Campaign Legal Center, one of the groups that sued Texas and represents some of the Justice Department’s fellow plaintiffs in the voter ID case. Under the Obama administration, she added, the Justice Department was “fully committed to the case.”

“They were full partners,” Ms. Lang said. “This was their case as much as ours.”

The Texas Legislature is considering a new voter ID bill that will allow those who have difficulty obtaining the appropriate IDs to vote as long as they sign an affidavit and show more widely available types of identification, including a utility bill or a bank statement. In documents filed on Monday, the Justice Department said that in light of the recently filed bill, it was withdrawing its discriminatory-intent claim to allow “the Texas Legislature the opportunity to rectify any alleged infirmities with its voter identification law.”

The agency added that the Supreme Court has emphasized that “federal courts should allow state legislatures the first opportunity to remedy voting rights violations.”