MINNEAPOLIS — The Minnesota Supreme Court on Wednesday dismissed a lawsuit seeking to bar President Trump from the state’s 2024 primary ballot under a constitutional provision that forbids those who “engaged in insurrection” from holding office.

The state’s high court declined to become the first in history to use Section 3 of the 14th Amendment to prevent someone from running for the presidency. The court dodged the central question of the lawsuit — whether Mr. Trump’s role in the January 6, 2021, breach of the Capitol disqualifies him from the presidency — by ruling that state law allows parties to put whomever they want on the primary ballot.

“There is no state statute that prohibits a major political party from placing on the presidential nomination primary ballot, or sending delegates to the national convention supporting, a candidate who is ineligible to hold office,” Chief Justice Natalie Hudson ruled. Two justices had recused themselves from the November 2 hearing.

The court left open the possibility that plaintiffs could try again to knock Mr. Trump off the general election ballot in November. The Minnesota challenge was filed by the liberal group Free Speech For People, which did not immediately comment on the decision or say whether they will appeal it.

The ruling is the first to come in a series of lawsuits filed by liberal groups that are seeking to use Section 3 to end the candidacy of the frontrunner in the Republican presidential primary.

On his social media platform, Truth Social, Mr. Trump said “Ridiculous 14th Amendment lawsuit just thrown out by Minnesota Supreme Court.” He added, “Congratulations to all who fought this HOAX!”

The provision at issue bars from office anyone who swore an oath to the constitution and then “engaged in insurrection” against it. It was mainly used to prevent former confederates from taking over state and federal government positions after the Civil War.

The plaintiffs in the cases contend that Section 3 is simply another qualification for the presidency, just like the Constitution’s requirement that a president be at least 35 years old. They filed in Minnesota because the state has a quick process to challenge ballot qualifications, with the case heard directly by the state’s highest court.

Mr. Trump’s attorneys argued that Section 3 has no power without Congress laying out the criteria and procedures for applying it, that the January 6 attack doesn’t meet the definition of insurrection and that the former president was simply using his free speech rights. They also argued that the clause doesn’t apply to the office of the presidency, which is not mentioned in the text.

Parallel cases are being heard in other states, including Colorado, where a state judge has scheduled closing arguments for next week.

Many legal experts expect the issue to eventually reach the United States Supreme Court, which has never ruled on Section 3.