The signs were stark, in bold, capital letters at early voting sites in Louisiana on Saturday: “ATTENTION! NOTICE OF CANCELLATION.”

The normally scheduled House primaries had been scrapped, the bulletins said, and any votes cast for those races would not be counted. It was an unusual message directed at Louisianians who showed up for the first day of early voting, and a reflection of the dizzying scramble that is playing out after the Supreme Court struck down the state’s congressional map.

The court’s ruling prompted Gov. Jeff Landry, a Republican, to delay House primaries, but to allow other contests to move ahead on May 16. The governor’s directive faces legal challenges and mounting concern about voter confusion.

Some early glimpses of bewilderment came into focus on Saturday. Outside of Baton Rouge City Hall, Linda Thomas felt compelled to double check with a poll worker that she would be able to have her vote counted.

“That was my biggest concern,” said Ms. Thomas, who voted along with her daughter and great-granddaughter. “Would my vote count?”

The Supreme Court’s decision, which said that Louisiana’s map was an illegal racial gerrymander, could have major national implications that extend well beyond this year’s elections. But some of the most immediate effects are in the state at the center of the case, where both parties are now bracing for a turbulent election season.

“It’s a huge mess,” said Lionel Rainey III, a Republican strategist in Louisiana. “It’s a nightmare scenario for election officials, and there is going to be unquestionably mass confusion at the polls.”

Some political organizations, such as the Democratic National Committee, have scrambled to set up efforts to educate voters on the shifting timelines.

“People keep calling us — I mean, voters think that the election has been canceled,” said Ashley Shelton, the president of the Power Coalition for Equity and Justice, a local civil rights organization in Louisiana.

Republicans are also taking to social media to encourage their constituents to vote. The campaign of one Senate candidate, John Fleming, Louisiana’s state treasurer, was sending out texts and emails to try to inform voters that the Senate primary was moving forward on schedule.

“Some people think that all races are delayed,” he said in an interview on Saturday, warning that some confused voters “could end up just saying: To heck with it.”

David Becker, the executive director of the Center for Election Innovation and Research, a nonpartisan group that advises election officials, warned that “radical change like this results in voter confusion.”

“And voter confusion, often if not almost always, results in lower turnout,” he added.

The upheaval in Louisiana is the latest turn in a lengthy fight over congressional boundaries.

With Republicans defending a narrow House majority, voters across the country had already been caught in a partisan redistricting battle started by President Trump and Republican lawmakers in Texas that has extended to Democratic-led states.

The Supreme Court ruling on Wednesday raised the standard for what can be considered an intentional dilution of minority voter power, opening the possibility for another wave of redistricting in Southern states with significant numbers of Black voters.

Two Republican-led Southern states, Alabama and Tennessee, are convening special legislative sessions ahead of their primary elections to consider new maps that would likely dilute at least one majority-Black district in each state. That could upend existing primary campaigns and send voters into new districts, paired with different communities and unfamiliar representatives.

Louisiana has been mired in litigation over its maps for years since it first redrew them following the 2020 census. But the state’s primary was already ripe for confusion because of a separate change. While Louisiana had long held open primaries that advance the top two candidates, regardless of party affiliation, it shifted to closed party primaries long before the Supreme Court ruling.

“That was going to be confusing in and of itself” for some voters, said Cameron Henry, the president of the Louisiana State Senate, and a Republican. As the Republican majority considered how to handle the aftermath of the ruling, he added, “anything we can do to reduce the amount of confusion that’s already surrounded this election cycle would be beneficial for everybody.”

The Louisiana secretary of state’s office did not respond to requests for comment about voter education plans in the state. But in her statement announcing the primary change, Secretary of State Nancy Landry (who is not related to the governor) said notices would be placed at early voting locations and shared a similar message online.

Mr. Landry and other state officials have argued that it would be unconstitutional to operate another House election under a map rejected by the nation’s highest court. “Louisiana is following the law,” he wrote on social media on Friday.

Critics see politics as an overarching factor: A new Louisiana map is likely to help Republicans win control of at least one additional district. Because Black voters in the South have largely backed Democrats in recent years, splitting up or diluting majority-Black districts is likely to hand Republicans an advantage.

Changing the timing and mechanics of the election so late in process is a massive logistical undertaking, according to former election officials. Voter logs need to be updated and new ballots printed, among other tasks.

“People have this perception that there’s two days a year that elections happen, but they have no idea of all the things that go into elections,” said Kathy Boockvar, the former top elections official in Pennsylvania and a Democrat. She said that, in her experience in Pennsylvania, work for a May primary began in December.

Adding another full primary election, Ms. Boockvar said, would also further tax the “thinly stretched, underfunded, understaffed and overworked” election officials, require more poll worker recruitment and likely add a significant new cost to the state.

While special elections for resigning or deceased candidates can sometimes lead to a bifurcated primary calendar, splitting up ongoing elections in Congress has little precedent in modern American elections. Those challenging the legality of the delayed House primaries have pointed to absentee ballots that have already been completed for the primary.

The change has rattled the closely-watched G.O.P. Senate primary in which Senator Bill Cassidy, a second-term incumbent who voted to convict Mr. Trump in his impeachment trial after the Jan. 6, 2021, attack on the U.S. Capitol, is laboring to hold off challenges from Mr. Fleming and Representative Julia Letlow, who has the endorsement of both Mr. Landry and Mr. Trump.

“The way that the election has transpired — that has almost treated the voters with disrespect,” Mr. Cassidy told reporters on Saturday after casting his ballot early. “You’ve got to be really focused to understand that there’s an election that starts today.”

Danny Bosch, 32, a Baton Rouge lawyer who voted on Saturday, said he understood that the House contests were being delayed, but that he made a selection for that office anyway, because “it was there” as he cast his ballot.

“I’m sure a lot of people are confused about it,” he said of the primary election.