Missouri voters cannot weigh in on whether to keep congressional district boundaries that were redrawn to benefit Republicans, Secretary of State Denny Hoskins said on Tuesday, even though opponents of the new map had gathered thousands of signatures seeking a statewide vote.

The decision, which was announced on Election Day while primary voters were at the polls, was widely expected to be challenged in court. Opponents of the redrawn map have signaled that they will ask judges to place the referendum on the November ballot and to revert to the old congressional map for the general election.

“Secretary of State Hoskins is making a last desperate attempt to silence the people’s voice in Missouri,” said Richard von Glahn, the executive director of People Not Politicians Missouri, the group that proposed the referendum. “We’ve fought back against politicians for the last year,” he added in a statement, “and we won’t stop now.”

The status of Missouri’s congressional districts has been unclear for months, even as candidates were campaigning and voters casting primary ballots in the newly redrawn districts.

Mr. Hoskins, a Republican, waited months to make a decision on whether the proposed referendum qualified for the ballot, drawing complaints from opponents of redistricting. Those people and groups insisted that they had submitted more than enough signatures and that the old district lines should apply until a referendum is held.

Mr. Hoskins said he believed that Missouri law did not allow for a congressional map to be challenged in a referendum and that he was prepared to defend that decision in court.

He declined to say how many valid signatures had been submitted and whether that number would have been sufficient to place the question on the ballot had he found the referendum to be constitutional.

“At issue is not the number of signatures turned in,” he told reporters, “but the fact that the referendum itself is null and void by virtue of the fact that it is unconstitutional.”

Missouri law allows residents to gather signatures to challenge legislation. If enough signatures are gathered, the legislation is paused until a statewide vote is held. By waiting to make a decision on the petitions until the deadline on Tuesday, Mr. Hoskins might have increased the odds that the new map is used in November, even if the courts eventually decide that voters should weigh in on the referendum.

Residents started collecting signatures last year shortly after Republican lawmakers passed the new congressional map, which was designed to flip one of the state’s two Democratic-held U.S. House seats. Missouri was among the first states to join President Trump’s national push to redraw district boundaries to improve Republicans’ odds of keeping House control in the midterms. Some Democratic-led states responded by proposing new boundaries of their own.

The Missouri Supreme Court ruled that lawmakers had acted within their authority when they redrew the map outside the usual once-a-decade cycle.

The map passed by Republicans last year sliced the core of Kansas City, Mo., into three districts and left Representative Emanuel Cleaver, a long-serving Democrat who was also Kansas City’s first Black mayor, with a Republican-leaning district that includes faraway rural counties. The new map did not significantly change the makeup of Missouri’s other Democratic-held district, in the St. Louis area.

The fate of Missouri’s map could help determine partisan control of the House during the final two years of Mr. Trump’s term.

After a brief pause, redistricting efforts ramped up again this spring after the Supreme Court raised the bar for bringing challenges under the Voting Rights Act of 1965. Several Republican-led Southern states redrew their maps after the ruling, positioning the party to pick up several seats in the midterms.