Federal prosecutors investigating former President Donald J. Trump’s attempts to overturn the 2020 election have questioned multiple witnesses in recent weeks — including Mr. Trump’s son-in-law, Jared Kushner — about whether Mr. Trump had privately acknowledged in the days after the 2020 election that he had lost, according to four people briefed on the matter.
The line of questioning suggests prosecutors are trying to establish whether Mr. Trump was acting with corrupt intent as he sought to remain in power — essentially that his efforts were knowingly based on a lie — evidence that could substantially bolster any case they might decide to bring against him.
Mr. Kushner testified before a grand jury at the federal courthouse in Washington last month, where he is said to have maintained that it was his impression that Mr. Trump truly believed the election was stolen, according to a person briefed on the matter.
The questioning of Mr. Kushner shows that the federal investigation being led by the special counsel Jack Smith continues to pierce the layers closest to Mr. Trump as prosecutors weigh whether to bring charges against the former president in connection with the efforts to promote baseless assertions of widespread voter fraud and block or delay congressional certification of Joseph R. Biden Jr.’s Electoral College victory.
A spokesman for Mr. Kushner and a spokesman for Mr. Trump did not respond to an email seeking comment.
But others in Mr. Trump’s orbit who interacted with him in the weeks after the 2020 election, who have potentially more damaging accounts of Mr. Trump’s behavior, have been questioned by the special counsel’s office recently.
Among them is Alyssa Farah Griffin, the White House communications director in the days after the 2020 election. Repeating an account she provided last year to the House select committee on Jan. 6, she told prosecutors this spring that Mr. Trump had said to her in the days after the election: Can you believe I lost to Joe Biden?
“In that moment I think he knew he lost,” Ms. Griffin told the House committee.
Ms. Griffin’s lawyer, Charles J. Cooper, declined to comment.
Still other witnesses have been asked whether aides told Mr. Trump that he had lost, according to people familiar with some of the testimony, another topic explored by the House committee. Witnesses have also been asked about things the former president was telling people in the summer months leading up to Election Day and even as far back as the spring of 2020, when the coronavirus pandemic began.
The question of Mr. Trump’s intent could be important in strengthening the hand of prosecutors if they decide to charge Mr. Trump in the case. It is not known what charges they might be considering, but the House select committee, controlled by Democrats, referred a number of possible charges to the Justice Department last year, including inciting an insurrection, conspiracy to defraud the United States and obstructing an act of Congress.
Mr. Trump is already facing federal charges brought by Mr. Smith in connection with classified documents taken from the White House, and he is under indictment in New York on charges related to hush-money payments to a pornographic film actress before the 2016 election. A district attorney in Fulton County, Ga., has been investigating efforts by Mr. Trump and his allies to reverse his 2020 election loss in Georgia.
Legal experts and former federal prosecutors say that establishing Mr. Trump’s mind-set to show he knew that what he was doing was wrong would give prosecutors in Mr. Smith’s election-focused inquiry a more robust case to put in front of a jury if they choose to bring charges.
Prosecutors do not need hard evidence of a defendant saying: I know that I am breaking the law. But their cases are made stronger when they can produce evidence that the defendant knows there is no legal or factual basis for a claim but goes ahead with making it anyway.
Daniel Zelenko, a partner at the firm Crowell & Moring and a former federal prosecutor, said that being able to cite a defendant’s own words can go a long way in helping prosecutors convince a jury that the defendant should be convicted.
“Words are incredibly powerful in white-collar cases because in a lot of them you’re not going to hear from a defendant, as they are seldom going to take the stand,” he said. “So, having those words put in front of a jury gives them more importance and makes them more consequential.”
Andrew Goldstein, the lead prosecutor for the obstruction investigation into Mr. Trump and a partner at the law firm Cooley, said there were other benefits to having Mr. Trump’s own statements that were critical in such a potentially weighty case.
“Just as important, if the Department of Justice has this kind of evidence, it could help justify to the public why charges in this case would be necessary to bring,” Mr. Goldstein said.
Some aides and allies who interacted with Mr. Trump in the days after the election have previously disclosed that Mr. Trump indicated that he knew he lost the election. In testimony before the House select committee, the chairman of the Joint Chiefs of Staff, Gen. Mark A. Milley, said that in an Oval Office meeting in late November or early December 2020, Mr. Trump acknowledged that he had lost the election.
“He says words to the effect of: Yeah, we lost, we need to let that issue go to the next guy,” Mr. Milley said, adding: “Meaning President Biden.”
“And the entire gist of the conversation was — and it lasted — that meeting lasted maybe an hour or something like that — very rational,” General Milley said. “He was calm. There wasn’t anything — the subject we were talking about was a very serious subject, but everything looked very normal to me. But I do remember him saying that.”
General Milley said, though, that in subsequent meetings Mr. Trump had increasingly discussed how the election was stolen from him.
“It wasn’t there in the first session, but then all of a sudden it starts appearing,” General Milley said.
A text message from early December 2020 between some of Mr. Trump’s lawyers, disclosed on Tuesday night, shows Mr. Trump searching at that time for reports of how the election was stolen, if they had not been substantiated. The text was sent by one of Mr. Trump’s personal lawyers, Boris Epshteyn, to other members of the legal team, including Rudolph W. Giuliani. Mr. Epshteyn said that he was relaying a direct message from Mr. Trump’s communications aide Jason Miller.
“Urgent POTUS request need best examples of ‘election fraud’ that we’ve alleged that’s super easy to explain,” the text message said. “Doesn’t necessarily have to be proven, but does need to be easy to understand.”
He continued, “Is there any sort of ‘greatest hits’ clearinghouse that anyone has for best examples? Thank you!!!”
That same day, Mr. Giuliani replied: “The security camera in Atlanta alone captures theft of a minimum of 30,000 votes which alone would change result in Georgia.” He continued, “Remember it will live in history as the theft of a state if it is not corrected by State Legislature.”
The text messages were made public in connection with a defamation lawsuit being brought by two Georgia election workers against Mr. Giuliani.
Mr. Trump has continued to maintain publicly, without any credible evidence, that he lost his re-election bid because of fraud and has defended the motivations of the mob that sought to disrupt the certification of his loss on Jan. 6, 2021.
Even if Mr. Kushner, a key White House adviser to Mr. Trump, did not provide prosecutors with evidence to bolster any charge they might bring, his testimony gives them a sense of what he might say if called by the defense to testify in any trial.
The New York Times reported in February that Mr. Smith’s office had subpoenaed Mr. Kushner and his wife, Ivanka Trump, to testify before the grand jury. The special counsel’s office has yet to question her before the grand jury. Ms. Trump testified before the House committee last year.
The House Jan. 6 committee determined that Mr. Trump’s decision to declare victory on election night even though the votes had not been fully counted yet was not spontaneous, but rather a “premeditated” plan promoted by a small group of his advisers.
The panel found evidence, for instance, that Tom Fitton, the head of the conservative group Judicial Watch, was in direct communication with Mr. Trump even before Election Day and understood that he “would falsely declare victory on election night and call for the vote counting to stop.”
Similarly, congressional investigators unearthed an audio recording made on Oct. 31, 2020, of Stephen K. Bannon, a former adviser to Mr. Trump, who told associates that the president was going to summarily declare he had won the election.
“But that doesn’t mean he’s a winner,” Mr. Bannon said in the recording. “He’s just going to say he’s a winner.”
Mr. Bannon was issued a subpoena last month to appear before the grand jury in Washington investigating Mr. Trump’s efforts to overturn the election.
In the last two years, reported accounts of Mr. Trump’s final months in office included his former White House chief of staff, Reince Priebus, describing to a friend how Mr. Trump had acted out a script the month before the election that he planned to deliver on election night, saying he had won if he was ahead in the early returns.
On election night, Mr. Giuliani — who, witnesses testified to the House committee, appeared inebriated — wanted Mr. Trump to follow through with the plan to simply declare victory. Mr. Giuliani was the sole adviser encouraging Mr. Trump to pursue that course, the committee found.
Among those telling Mr. Trump on election night that it was too early to know if he had won or lost were his campaign manager, Bill Stepien, and Mr. Miller, the communications adviser. In the weeks that followed, several other aides and advisers told Mr. Trump there was no evidence of fraud sufficient to change the results of the election, including William P. Barr, his former attorney general.
Alan Feuer and Jonathan Swan contributed reporting.