In a lawsuit filed on Wednesday, a Democratic super PAC wants the Federal Election Commission to take action against Donald J. Trump for all but running for president in 2024 without declaring his candidacy.

The lawsuit comes more than four months after American Bridge filed a complaint with the F.E.C. against Mr. Trump. By failing to file a statement of candidacy, he has behaved like a presidential candidate in 2024 while avoiding oversight by the commission.

In the past year, Mr. Trump has held rallies ostensibly in support of Republicans running for local, statewide, and congressional races. Furthermore, he has given several interviews in which he has sounded like a candidate. While it is unclear when Mr. Trump will make a formal announcement, he has accelerated his campaign, planning to direct damaging revelations from investigations into his attempt to overturn the election result.

According to the lawsuit, Mr. Trump has an advantage as a candidate without a formal campaign committee due to the agency’s inaction.

According to the suit, Mr. Trump’s efforts aim to conceal his candidacy, leaving the group and voters “in the dark” about his contributions and expenditures.

According to the lawsuit, his continued fund-raising for his political groups “gives him a competitive edge” over his Democratic opponent.

Within 30 days, the group urged the F.E.C. to take action against Trump. If the commission does not take action, additional action should be taken against Mr. Trump and the commission.

A request for comment from the F.E.C. was not immediately responded to.

American Bridge’s lawyers claim that if the agency had acted swiftly to their complaint in March, Mr. Trump would have been required to register a principal campaign committee and disclose his campaign activities. In addition, they said that the former president’s PAC, Save America, has been spending money on candidate-related activities for a year. Mr. Trump is not subject to the disclosures that the commission requires of candidates, so the group argues they are at a disadvantage in conducting opposition research.

Several remarks the former president made in recent months hinted at another presidential run were compiled in the lawsuit.

He replied, according to the lawsuit, “the 45th and 47th.” In February, he told a conservative group, “we’ll be doing it again a third time,” and referred to his wife Melania Trump as “the future first lady.”

In a July interview with New York magazine, he said that “in my own mind, I’ve already made that decision.”

Mr. Trump’s spokesman did not respond to a request for comment.

As of now, it is unclear whether the suit will work its way through the courts in time to affect the commission or Mr. Trump. Several lawsuits have been filed to force the F.E.C. to act on campaign finance issues. Several of those lawsuits are still pending.