Rudolph W. Giuliani, who served as former President Donald J. Trump’s private lawyer, was interviewed final week by federal prosecutors investigating Mr. Trump’s efforts to overturn the 2020 election, folks conversant in the matter stated.

The voluntary interview, which happened beneath what is called a proffer settlement, was a big improvement within the election interference investigation led by Jack Smith, the particular counsel, and the newest indication that Mr. Smith and his staff are actively in search of witnesses who may cooperate within the case.

The session with Mr. Giuliani, the folks conversant in it stated, touched on among the most necessary features of the particular counsel’s inquiry into the ways in which Mr. Trump sought to keep up his grip on energy after shedding the election to Joseph R. Biden Jr.

“The appearance was entirely voluntary and conducted in a professional manner,” stated Ted Goodman, a political adviser to Mr. Giuliani.

A proffer settlement is an understanding between prosecutors and people who find themselves topics of legal investigations that may precede a proper cooperation deal. The topics agree to offer helpful data to the federal government, generally to inform their facet of occasions, to stave off potential expenses or to keep away from testifying beneath subpoena earlier than a grand jury. In alternate, prosecutors agree to not use these statements towards them in future legal proceedings until it’s decided they had been mendacity.

Prosecutors working for Mr. Smith requested Mr. Giuliani about a plan to create fake slates of pro-Trump electors in key swing states that had been really received by Mr. Biden, one particular person conversant in the matter stated, talking on the situation of anonymity to debate an ongoing legal investigation. They targeted particularly on the position performed in that effort by John Eastman, one other lawyer who suggested Mr. Trump about methods to remain in workplace after his defeat.

Mr. Giuliani additionally mentioned Sidney Powell, a lawyer who was briefly tied to Mr. Trump’s marketing campaign and who made baseless claims a few cabal of international actors hacking into voting machines to steal the election from Mr. Trump, the particular person stated.

Ms. Powell, who was sanctioned by a federal judge for selling conspiracy theories concerning the voting machines, additionally took half in a gathering within the Oval Office in December 2020 throughout which Mr. Trump was offered with a brazen plan — opposed by Mr. Giuliani — to use the military to seize control of voting machines and rerun the election.

The particular person stated that prosecutors additional requested Mr. Giuliani concerning the scene on the Willard Hotel days earlier than the assault on the Capitol. Mr. Giuliani and a bunch of shut Trump advisers — amongst them, Mr. Eastman, Mr. Trump’s former chief strategist Stephen Ok. Bannon and Mr. Trump’s present adviser Boris Epshteyn — had gathered on the resort, close to the White House, to debate methods earlier than a violent mob stormed the Capitol on Jan. 6, 2021, disrupting the certification of Mr. Biden’s victory over Mr. Trump.

The proffer session with Mr. Giuliani, components of which had been reported earlier by CNN, got here as Mr. Smith’s staff pressed forward with its election interference inquiry of Mr. Trump even because it prepares for the former president’s trial on separate charges of placing nationwide safety secrets and techniques in danger and obstructing authorities efforts to get well categorized paperwork.

The prosecutors have been bringing witnesses earlier than a grand jury and conducting separate interviews of others as they search to assemble a fuller image of the assorted methods wherein Mr. Trump and his allies had been selling baseless claims that the election had been stolen from him and in search of to reverse his electoral defeat.

In some instances, they seem like gauging whether or not they can elicit helpful data with out essentially agreeing to formal cooperation offers.

Last week, The New York Times reported that prosecutors had been in negotiations to reach a proffer agreement with Michael Roman, the previous director of Election Day operations for Mr. Trump’s 2020 marketing campaign. Mr. Roman was additionally instrumental in serving to put collectively the so-called faux elector plan.

The push to assemble slates of pro-Trump electors from swing states received by Mr. Biden is one in every of a lot of parts of Mr. Smith’s investigation. Prosecutors have additionally scrutinized whether or not Mr. Trump and his allies bilked donors by elevating cash by way of false claims of election fraud, examined efforts to make use of the Justice Department to present credence to election-fraud claims and sought to piece collectively an in depth image of the position performed by Mr. Trump in inciting the assault on the Capitol and the disruption of the congressional certification of his loss.

It stays unclear whether or not Mr. Giuliani will face expenses within the particular counsel’s investigation. He can be beneath scrutiny on lots of the identical topics by the district lawyer in Fulton County, Ga., who’s pursuing a wide-ranging investigation into Mr. Trump’s effort to reverse his election loss in that swing state.

As a part of Mr. Smith’s inquiry, prosecutors questioned Mr. Roman’s deputy, Gary Michael Brown, final week in entrance of a grand jury in Federal District Court in Washington that has been investigating the makes an attempt by Mr. Trump and his allies to overturn the election. Federal prosecutors on Wednesday are additionally scheduled to interview Brad Raffensperger, the secretary of state of Georgia, who took a call from Mr. Trump in early January 2021 throughout which the previous president requested him to “find” enough votes that will put him excessive within the election in that state.

A longtime ally of Mr. Trump who served two phrases as New York City’s mayor, Mr. Giuliani successfully led the previous president’s makes an attempt to overturn his defeat within the final presidential race and has for months been a chief focus of the Justice Department’s broad investigation into the postelection interval. His name has appeared on several subpoenas despatched to former aides to Mr. Trump and to a number of Republican state officers concerned within the plan to create faux slates of electors.

Last 12 months, shortly earlier than Mr. Smith was appointed to his job as particular counsel, the Justice Department issued a subpoena to Mr. Giuliani for data associated to his illustration of Mr. Trump, together with those who detailed any funds he had obtained. A gaggle of federal prosecutors together with Thomas Windom had been pursuing varied strands of the inquiry into Mr. Trump’s efforts to stay in energy earlier than Mr. Smith’s appointment they usually proceed to play key roles within the investigation.

Among the issues that prosecutors have been analyzing are the inside workings of Mr. Trump’s fund-raising car, Save America PAC. The data subpoenaed from Mr. Giuliani may embody some associated to funds made by the PAC, in accordance with an individual conversant in the matter.

More lately, prosecutors have been asking questions on Mr. Trump’s false claims that his defeat within the election was brought on by widespread fraud, and the way he aggressively raised cash off these claims. The prosecutors have drilled down on the difficulty of whether or not folks round Mr. Trump knew that he had misplaced the race, however continued elevating cash off the fraud claims anyway.

The House choose committee that investigated the assault on the Capitol on Jan. 6 first raised questions publicly about Mr. Trump’s fund-raising, and the particular counsel’s staff has picked up on that thread. Among different questions they’ve requested witnesses is whether or not their attorneys are being paid for by the political motion committee that turned a repository for cash raised off Mr. Trump’s false claims of widespread fraud.

Investigators have walked by way of a timeline with varied witnesses, together with asking folks about election evening and what Mr. Giuliani might have been telling Mr. Trump earlier than his defiant speech declaring he had received the election, in addition to about Jan. 6 and Mr. Trump’s actions that day.

The particular counsel’s workplace has targeted on Mr. Trump’s mind-set and who was telling him he misplaced, in accordance with folks conversant in the questions. Among the questions has been whether or not there have been issues raised amongst folks working with the marketing campaign as to the language utilized in tv adverts about fraud in December 2020, and who signed off on the advert copy.

Prosecutors additionally subpoenaed former Vice President Mike Pence, who was a key focus of Mr. Trump’s efforts to remain in energy as Mr. Trump tried to stress him to make use of his ceremonial position overseeing congressional certification to dam Mr. Biden from being licensed.