Representative George Santos, the Republican from New York whose unexpected victory in November was quickly marred by revelations that he had lied or exaggerated about virtually his entire biography on the campaign trail, announced Monday that he was running for re-election.

In a statement announcing his campaign, Mr. Santos did not directly address the controversy that has surrounded him. Instead, he depicted himself as a “fighter” and political outsider who would work outside traditional Republican Party politics.

“We need a fighter who knows the district and can serve the people fearlessly, and independent of local or national party influence,” Mr. Santos said. “Good isn’t good enough, and I’m not shy about doing what it takes to get the job done.”

The announcement, first reported in The New York Post, follows months of speculation over Mr. Santos’s political future, with fellow Republican lawmakers calling for his resignation, and federal and state prosecutors and his colleagues in Congress investigating his falsehoods on the campaign trail and his finances.

Last month, Mr. Santos filed paperwork indicating his intent to run for re-election, but his announcement on Monday was his first public declaration of his 2024 campaign.

Mr. Santos, whose victory helped Republicans take control of the House, has remained defiant throughout the controversy.

Though he has admitted to fabricating some parts of his résumé and biography, Mr. Santos has stood by other apparent falsehoods and insisted that the inquiries into him would find no criminal wrongdoing. Still, for months, the first-term Republican remained publicly ambivalent about whether he would run again, calling questions about a re-election bid premature.

Mr. Santos enters the race with a significant cash crunch. As of the end of last month, his campaign had just over $25,000 on hand, according to reports filed with the Federal Election Commission.

While other first-term Republicans in New York battleground districts raised hundreds of thousands in the first three months of the year, Mr. Santos raised only $5,333.26. During that same period he refunded nearly $8,400, bringing his fund-raising total into the negative.

That is less than Mr. Santos raised during his first run for office in 2020, when Mr. Santos was virtually unknown, and he reported receiving about $7,000 in the same three-month period.

Mr. Santos was already expected to face a competitive race even before he was mired in scandal and his path forward was clouded by investigations.

Democrats, eager to reverse losses in reliably liberal New York that cost them their hold on Congress, were eyeing Mr. Santos’s suburban district, which covers northern Nassau County on Long Island and a small section of northeast Queens, and had favored Democrats for a decade until Mr. Santos’s victory last year.

But Mr. Santos’s seat became even more of a priority for Democrats after The New York Times and other news outlets published revelations that he had omitted key details from his financial disclosures and misled voters about his education, his professional background, his heritage and his ties to tragedies like the Pulse nightclub shooting and the Sept. 11 attacks.

Subsequent reporting uncovered a number of irregularities in his campaign filings, including an unusual pattern of payments for $199.99, an unregistered fund that purported to be raising huge amounts for Mr. Santos and thousands of dollars in unexplained expenses.

The F.B.I., federal prosecutors in Brooklyn and the Nassau County district attorney’s office are now all investigating Mr. Santos’s campaign finances and how Mr. Santos operated his business, the Devolder Organization, about which he has disclosed little information.

The House Ethics Committee, which is split evenly between Republican and Democratic representatives, has also opened an inquiry into whether Mr. Santos failed to properly fill out his financial disclosure forms, violated federal conflict of interest laws or engaged in other unlawful activity during his 2022 congressional campaign.