After federal authorities raided the home of Mayor Eric Adams’s chief fund-raiser on Nov. 2, a broad criminal inquiry into the fund-raising practices of Mr. Adams’s 2021 campaign spilled into public view.

Federal prosecutors and the F.B.I. are examining whether the campaign conspired with members of the Turkish government, including its consulate in New York, to receive illegal donations, according to a search warrant obtained by The New York Times.

Only two years into his first term, Mr. Adams has confronted a migrant crisis and the city’s struggle to recover from the pandemic, along with intense scrutiny of chaotic and violent conditions at the Rikers Island jail complex. But from a personal and a public relations perspective, the investigation into his fund-raising poses perhaps the steepest challenge yet for the mayor, who has already raised more than $2.5 million for his re-election bid in 2025.

Here’s what we know about the investigation.

The full scope of the federal criminal inquiry is not yet clear, but the investigation has focused at least in part on whether Mr. Adams’s 2021 campaign conspired with the Turkish government and Turkish nationals to receive illegal donations.

According to the search warrant, federal prosecutors and the F.B.I. are also examining the role of a Brooklyn building company, KSK Construction, which is owned by Turkish immigrants and which organized a fund-raising event for Mr. Adams in May 2021.

The search warrant also indicated that investigators were reviewing whether anyone affiliated with the mayor’s campaign provided any legal or illegal benefits — which could range from governmental action to financial favors — to the construction company and its employees, or to Turkish officials.

The search warrant was executed on Nov. 2, the day that federal agents raided the Brooklyn home of Mr. Adams’s chief fund-raiser, Brianna Suggs.

Ms. Suggs was an inexperienced 23-year-old former intern when Mr. Adams’s campaign tapped her to run its fund-raising operation for his successful 2021 mayoral bid. Now 25, she has become embroiled in a sprawling federal investigation.

Even before graduating from Brooklyn College in 2020, Ms. Suggs was on Mr. Adams’s staff in his previous job as Brooklyn borough president. She has a close relationship both with Mr. Adams and his top aide and confidante, Ingrid Lewis-Martin, and she impressed some who interacted with her at campaign fund-raisers as smart and easy to work with.

After the election, Ms. Suggs remained an essential cog in Mr. Adams’s fund-raising machine. She has not been accused of wrongdoing.

During the raid of her house in Crown Heights, federal agents seized two laptop computers, three iPhones and a manila folder labeled “Eric Adams.”

Mr. Adams has not been accused of wrongdoing. The mayor was in Washington, D.C. on the morning of the raid and had plans to speak with White House officials and members of Congress about the migrant crisis. He abruptly canceled the meetings and returned to New York.

He later said he hurried back to be present for his team and to show support for Ms. Suggs.

“Although I am mayor, I have not stopped being a man and a human,” he said, but added that he did not speak with his aide on the day of the raid.

Days after Ms. Suggs’s house was raided, federal agents approached Mr. Adams after an event in Manhattan, asked his security detail to step aside and got into his SUV with him. The F.B.I. seized at least two cellphones and an iPad from the mayor, copied the devices and returned them within days, the mayor’s lawyer said.

After The Times reported on the seizure, a lawyer for Mr. Adams and his campaign said in a statement that the mayor was cooperating with federal authorities and had already “proactively reported” at least one instance of improper behavior.

“After learning of the federal investigation, it was discovered that an individual had recently acted improperly,” said the lawyer, Boyd Johnson. “In the spirit of transparency and cooperation, this behavior was immediately and proactively reported to investigators.”

Mr. Johnson reiterated that Mr. Adams had not been accused of wrongdoing and had “immediately complied with the F.B.I.’s request and provided them with electronic devices.”

Mr. Johnson did not identify the individual who was alleged to have acted improperly. He also did not detail the conduct reported to authorities or make clear whether the reported misconduct was related to the seizure of the mayor’s devices. A spokesman for Mr. Adams’s campaign said it would be inappropriate to discuss those issues because the investigation is ongoing.

In his own statement, Mr. Adams said, “As a former member of law enforcement, I expect all members of my staff to follow the law and fully cooperate with any sort of investigation — and I will continue to do exactly that.”

He added that he had “nothing to hide.”

Federal authorities have been examining an episode involving Mr. Adams and the newly built Turkish consulate building in New York that occurred after he had won the Democratic nomination for mayor in the summer of 2021, according to three people with knowledge of the matter.

The Turkish consulate general planned to open its new building in time for the start of the United Nations General Assembly that September. But the Fire Department had not signed off on its fire safety plans, which had several problems — an obstacle that threatened to derail the Turkish government’s plans.

As Brooklyn borough president, Mr. Adams cultivated ties with local Turkish community members as well as Turkish government officials, who paid for part of a trip he made to Turkey in 2015. Mr. Adams has said he has visited Turkey six or seven times in all.

After winning the Democratic nomination, Mr. Adams was all but guaranteed to become the next mayor of New York. He contacted then-Fire Commissioner Daniel A. Nigro, relaying the Turkish government’s desire to use the building at least on a temporary basis, the people said.

The city ultimately issued a temporary certificate of occupancy for the building, near the United Nations in Midtown Manhattan.

The unusual intervention paved the way for the Turkish president, Recep Tayyip Erdogan, to preside over the grand opening of the $300 million, 35-story tower on his September 2021 visit to New York, despite the numerous flaws in its fire safety system, according to the people familiar with the matter and city records. The skyscraper reflected Turkey’s “increased power,” Mr. Erdogan said at its ribbon-cutting.

In response to questions from The Times, Mr. Adams’s campaign issued a statement from the mayor.

“As a borough president, part of my routine role was to notify government agencies of issues on behalf of constituents and constituencies,” Mr. Adams said. “I have not been accused of wrongdoing, and I will continue to cooperate with investigators.”