Months after a federal appeals court ruled that Texas lawmakers discriminated against African-American and Latino voters in passing a strict voter identification law, the Obama administration and civil rights groups are asking a judge to go a step further — by finding that the lawmakers did it on purpose.

“The discriminatory impact was not merely an unintended consequence” of the 2011 law, known as Senate Bill 14, Justice Department lawyers wrote in a brief filed late Friday. “It was, in part, SB 14’s purpose.”

The 45-page brief was part of the latest back-and-forth in the U.S. District Court for the Southern District of Texas — one of two legal fronts in a convoluted battle over identification requirements that were temporarily softened during November’s presidential election.

Texas Attorney General Ken Paxton refuted the plaintiffs’ arguments in his own filing Friday, accusing them of pushing a “false narrative.”

Paxton, Gov. Greg Abbott and other Republicans argue that the law was needed to bolster security at the ballot box by preventing voter fraud, but opponents cite the paucity of proven in-person voter fraud.

Judge Nelva Gonzales Ramos of Corpus Christi is tasked with deciding whether Texas violated the U.S. Constitution by intentionally discriminating against minority groups. Experts say such charges can be difficult to prove in court, but doing so would give critics ammunition in any future effort to put Texas back on the list of states needing federal approval before changing election laws.

In July, the U.S. 5th Circuit Court of Appeals ruled that Texas' 2011 voter ID law discriminated against minority groups, who were less likely to possess one of seven accepted types of identification. That was a violation of the federal Voting Rights Act, the majority ruled.

(For this year's election, Ramos ordered a temporary fix: Folks without ID could still vote if they presented an alternate form of ID and signed a form swearing a “reasonable impediment” kept them from obtaining photo ID.)

In September, Paxton appealed that decision to the U.S. Supreme Court, whose eight justices have not decided whether to take it up.

The 5th Circuit did not definitively rule on whether Texas discriminated on purpose.

In a 2014 ruling, Ramos found intent, but the appeals court instructed her to reconsider the evidence. The higher court’s majority wrote that some evidence "could support" Ramos’ conclusion, but called her conclusion “infirm.”

On Friday, the Justice Department argued that “a wealth of evidence” suggests that lawmakers consciously discriminated, including the state’s lengthy history of discrimination in elections and a shift in demographics that could threaten current officeholders.

The lawyers also argued that Texas Republicans took advantage of an “extraordinary degree of procedural irregularities” during the 2011 legislative session to address “a nearly nonexistent problem,” and they refused to answer direct questions about how the voting rules would affect minority voters.

In his filing, Paxton countered that plaintiffs had found no smoking gun.

“Despite their unlimited access to the confidential communications of Texas legislators who supported SB 14,” Paxton’s team wrote, “plaintiffs could proffer no evidence that any legislator harbored even a private intention to disenfranchise minority voters.”

President-elect Donald Trump’s November election victory has cast uncertainty over the ultimate outcome of the years-long voter ID battle, which has cost Texas taxpayers more than $3.5 million in litigation costs so far. Trump is poised to have the ability to fill the Supreme Court seat left vacant by Justice Antonin Scalia's death, and questions loom about how his Justice Department will handle voting rights issues.

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