After six weeks as a district attorney, Fani T. Willis is taking on a former president.

And not just that. In an interview about her newly announced criminal investigation into election interference in Georgia, Ms. Willis, the district attorney of Fulton County, made it clear that the scope of her inquiry would encompass the pressure campaign on state officials by former President Donald J. Trump as well as the activities of his allies.

“An investigation is like an onion,” she said. “You never know. You pull something back, and then you find something else.”

She added, “Anything that is relevant to attempts to interfere with the Georgia election will be subject to review.”

Ms. Willis, whose jurisdiction encompasses much of Atlanta, has suddenly become a new player in the post-presidency of Mr. Trump. She will decide whether to bring criminal charges over Mr. Trump’s phone call to Georgia’s secretary of state, Brad Raffensperger, asking him to “find” votes to erase the former president’s loss there, and other efforts by Trump allies to overturn the election results. The severity of the legal threat to Mr. Trump is not yet clear, but Ms. Willis has started laying out some details about the inquiry.

She and her office have indicated that the investigation will include Senator Lindsey Graham’s phone call to Mr. Raffensperger in November about mail-in ballots; the abrupt removal last month of Byung J. Pak, the U.S. attorney for the Northern District of Georgia, who earned Mr. Trump’s enmity for not advancing his debunked assertions about election fraud; and the false claims that Rudolph W. Giuliani, the president’s personal lawyer, made before state legislative committees.

She laid out an array of possible criminal charges in letters sent to state officials and agencies asking them to preserve documents, providing a partial map of the potential exposure of Mr. Trump and his allies. Mr. Trump’s calls to state officials urging them to subvert the election, for instance, could run afoul of a Georgia statute dealing with “criminal solicitation to commit election fraud,” one of the charges outlined in the letters, which if prosecuted as a felony is punishable by at least a year in prison.

The misinformation spread by Mr. Giuliani could prove problematic, as Ms. Willis said in her letters that she would review “the making of false statements to state and local governmental bodies.” Georgia law bars “any false, fictitious, or fraudulent statement” within “the jurisdiction of any department or agency of state government.”

Ms. Willis is also open to considering not just conspiracy but racketeering charges. As she put it in the interview, racketeering could apply to anyone who uses a legal entity — presumably anything from a government agency to that person’s own public office — to conduct overt acts for an illegal purpose. In this case, it applies to the pressure the president and his allies exerted on Georgia officials to overturn the election.

Ms. Willis has brought a novel racketeering case before. In 2014, as an assistant district attorney, she helped lead a high-profile criminal trial against a group of educators in the Atlanta public school system who had been involved in a widespread cheating scandal.

Racketeering cases tend to make people think of mob bosses, who have often been targets of the federal Racketeer Influenced and Corrupt Organizations Act, known as RICO, since it was enacted in 1970. Asked how racketeering applied in the cheating scandal and in an election case, Ms. Willis said, “I always tell people when they hear the word racketeering, they think of ‘The Godfather,’” but she noted that it could also extend to otherwise lawful organizations that are used to break the law.

“If you have various overt acts for an illegal purpose, I think you can — you may — get there,” she said.

Ms. Willis, 49, who easily won election last year, is the daughter of an activist defense lawyer who was a member of the Black Panthers, and she is also a veteran prosecutor who has carved out a centrist record. She views the case before her as a critical task.

“It is really not a choice — to me, it’s an obligation,” she said. “Each D.A. in the country has a certain jurisdiction that they’re responsible for. If alleged crime happens within their jurisdiction, I think they have a duty to investigate it.”

For their part, Mr. Trump and his allies are girding for a second criminal investigation, alongside an ongoing fraud inquiry before a grand jury in Manhattan. This week, Jason Miller, a senior adviser to Mr. Trump, called the Georgia investigation “simply the Democrats’ latest attempt to score political points by continuing their witch hunt against President Trump, and everybody sees through it.”

Ms. Willis has many challenges before her, and not just relating to this inquiry. She replaced a controversial prosecutor who faced lawsuits accusing him of sexual harassment. In an overhaul of her office’s anti-corruption unit, which will handle the Trump investigation, she removed all eight lawyers and has since hired four, with a fifth on the way. The police in Atlanta, as elsewhere, are both maligned and demoralized, and 2020 was one of Atlanta’s deadliest years in decades. She must also decide how to proceed with the case of Rayshard Brooks, a Black man fatally shot by a white police officer last year.

“I have 182 open, unindicted homicides involving 222 defendants,” she said. “I have a sex crime unit that is backed up. But I am very capable of identifying great people to work in this office who are dedicated to the cause of making this county safer, and I do not get to be derelict in my duty, because I have other responsibilities.”

Clark D. Cunningham, a law professor at Georgia State University in Atlanta, said it appeared that Ms. Willis might be “pulling out all the stops” for the Trump case, “because of the range of the types of crimes that are mentioned in that letter,” he said, adding, “and particularly the talk about racketeering and conspiracy.”

The pressure campaign to overturn the Georgia election results began on Nov. 13, when Mr. Graham, a Trump ally from South Carolina, made a phone call to Mr. Raffensperger, Georgia’s secretary of state. Mr. Raffensperger, a Republican, later said that Mr. Graham had asked him if he had the authority to throw out all mail-in votes from particular counties, a suggestion the secretary of state rebuffed. (Mr. Graham disputed Mr. Raffensperger’s account.)

On Dec. 3, Mr. Giuliani, Mr. Trump’s personal lawyer, made an appearance before a Georgia State Senate committee, saying that “there’s more than ample evidence to conclude this election was a sham,” and laid out a number of false claims. Two days later, Mr. Trump called Brian Kemp, Georgia’s Republican governor, to press him to call a special session of the legislature to overturn the election. Mr. Trump then called Georgia’s Republican attorney general, Chris Carr, and pressured him not to oppose a legal attempt to challenge the elections results in Georgia and other swing states.

Because of the flurry of Trump calls, Ms. Willis said she believes that she is the only official with jurisdiction who does not have a conflict of interest. As she wrote in her letters to other public officials, “this office is the one agency with jurisdiction that is not a witness to the conduct that is the subject of the investigation.”

Even after Mr. Raffensperger recertified the election results on Dec. 7, Mr. Trump’s efforts intensified. Three days later, Mr. Giuliani testified virtually before a state House committee, repeating false claims that poll workers at an Atlanta arena had counted improper ballots stuffed in suitcases, when they were simply using the normal storage containers. “They look like they’re passing out dope,” he said during the hearing.

Gabriel Sterling, a top aide to Mr. Raffensperger, has derided the claims as a ridiculous, “‘Oceans 11’ type scheme,” adding, “This has been thoroughly debunked.”

Mr. Giuliani returned on Dec. 30, telling a Senate committee, “You had 10,315 people that we can determine from obituaries were dead when they voted,” and adding: “So, right away, that number you submitted to Washington is a lie. It’s not true! It’s false!” The numbers, however, were farcical; state officials have found only two instances in which votes were cast in the names of people who had died.

The pressure campaign culminated when Mr. Trump himself called Mr. Raffensperger on Jan. 2. “I just want to find 11,780 votes,” Mr. Trump said on the call, fruitlessly searching for ways to reverse his election loss.

Ms. Willis is also reviewing the departure of Mr. Pak, a Trump appointee. Shortly before Mr. Pak’s resignation, Mr. Trump’s acting deputy attorney general, Richard Donoghue, told Mr. Pak that the president was unhappy that he wasn’t pursuing voter fraud cases.

Ms. Willis has said that her office would request subpoenas “as necessary” when the next Fulton County grand jury convenes in March.

She appears undaunted. As she put it, “this is not a 9-to-5 job.” For her, lawyering is a family calling. Her father is John Clifford Floyd III, a longtime civil rights activist and defense lawyer.

“My dad was a single father that raised me,” she said. When she was a young girl in Washington, D.C., she said, her father would take her to court with him on Saturday mornings as he took on new clients who had been arrested the previous night.

“There was an old white Irish judge,” she recalled. “He would let me come sit up on the bench with him,” she recalled. While she was on his lap, the judge would ask her, “should we send them home, or are they going to the back?”

She decided then that she wanted to be a judge, but her father explained that she had to be a lawyer first. So her career ambition was set. While she embraces some of the prosecutorial reform efforts favored by the left, including diversion programs that keep some offenders out of jail, Ms. Willis has also said that she has a “conservative side” that separates her from the new wave of progressive prosecutors.

Heretofore, she has been best known for the Atlanta school case, in which 11 educators were convicted of racketeering and other crimes. The case drew criticism in some quarters for overreach.

“I’ve been criticized a lot for that case, but I’m going to tell you what I tell people if I’m taking criticism for defending poor Black children, because that’s mainly what we were talking about,” she said. The only chance many such children have to get ahead is through the public education system, she said, adding, “So if what I am being criticized for is doing something to protect people that did not have a voice for themselves, I sit in that criticism, and y’all can put it in my obituary.”