WASHINGTON - President Donald Trump’s lawyers set new conditions Friday on an interview with the special counsel and said the chances that the president would be voluntarily questioned were growing increasingly unlikely.

The special counsel, Robert Mueller, needs to prove before Trump would agree to an interview that he has evidence that Trump committed a crime and that his testimony is essential to completing the investigation, said Rudy Giuliani, the president’s lead lawyer in the case.

His declaration was the latest sign that the president’s lawyers, who long cooperated quietly with the inquiry even as their client attacked it, have shifted to an openly combative stance.

Giuliani acknowledged that Mueller was unlikely to agree to the interview demands. Mueller could subpoena Trump to answer questions if he does not agree to voluntarily sit for an interview. Giuliani left open the possibility that the president, who has said in the past that he would be eager to sit down with the special counsel, would still agree to be interviewed.

Giuliani appeared to be in part trying to shift responsibility onto the special counsel for the lengthy negotiations over an interview — and was most likely prolonging them himself.

“If they can come to us and show us the basis and that it’s legitimate and that they have uncovered something, we can go from there and assess their objectivity,” Giuliani said. He urged the special counsel to wrap up his inquiry and write an investigative report. He said Trump’s lawyers planned to write their own summary of the case.

A spokesman for the special counsel’s office declined to comment.

The president’s lawyers want Mueller to explain how the Justice Department gave him the authority to investigate possible obstruction of justice by the president in what began as a counterintelligence investigation into Russia’s election meddling. The order appointing Mueller authorized him to investigate possible links between Moscow’s interference and Trump associates, as well as any matters that arose from the inquiry.

The lawyers also want evidence that the special counsel exhausted every other investigative measure before asking the president to answer questions, and that he is the only person who could provide them with the information they are seeking.

The gambit by Giuliani was the latest maneuver in an all-out assault by the president and his legal team in recent months to alter public opinion about the inquiry. They have come to believe that, if the Democrats win control of the House in November, the chamber will vote on whether to begin the impeachment process no matter the outcome of Mueller’s investigation. So they want to sway Americans — and by extension, lawmakers.

To that end, Trump has publicly complained about the investigation more frequently in recent months — tweeting about a “witch hunt” 59 times since March, compared with 20 times in all of 2017 — and Giuliani regularly appears in the media attacking the investigation.

Trump’s lawyers are quietly more combative, too, contesting a request from the special counsel to interview John F. Kelly, the White House chief of staff. Emmet T. Flood, the lead White House lawyer in dealing with the investigation, has demanded to know what investigators want to ask Kelly and has tried to narrow the scope of their questions. A month after the request was made, Kelly has not been questioned, though a White House official said he was willing to be.

“That’s the new position. If they had made the request eight months ago, they would have said yes because they thought there was a group of people on Mueller’s team who had an open mind and were objective,” Giuliani said of the president’s previous lawyers, most of whom have left the legal team.

The effort appears to be bearing some fruit. According to a Washington Post-Schar School poll released on Friday, 45 percent of Americans disapprove of how Mueller is handling the investigation, a 14-point increase from January.

“Nobody is going to consider impeachment if public opinion has concluded this is an unfair investigation, and that’s why public opinion is so important,” Giuliani said.

The strategy is a departure from the legal team’s playbook during the first year of the special counsel investigation, when Trump’s lawyers were more cooperative. They waived executive privilege, handed over documents and made White House aides available for interviews, convinced that it would hasten the end of the inquiry.

But in April, Trump concluded that Mueller and Justice Department officials were determined to find wrongdoing after federal investigators in New York, acting on a referral from the special counsel, raided the office, hotel room and home of Trump’s longtime personal lawyer Michael D. Cohen.

After the raid, Trump decided to double down on his more aggressive strategy, according to people close to him. He hired Giuliani to replace his lawyer John M. Dowd, who had convinced Trump of the value of the earlier, more cooperative approach. Giuliani immediately began a public relations assault on Mueller. Flood, who is known for his strong view of the president’s powers to shield his communications and documents from investigators, was brought on in May.

Giuliani has sown doubt and confusion by pushing dubious theories about the case. He has made claims like accusing Mueller’s office, without evidence, of trying to frame Trump. Giuliani has also pushed unfounded theories, like an assertion that the FBI implanted a spy in Trump’s campaign.

The president and his lawyers have also tried to undermine key witnesses like James B. Comey, the former FBI director fired by Trump, to force the public to decide whether to believe them or the president. That is a tall task — the president’s penchant for half-truths, exaggerations and outright falsehoods is well established.

But Trump and his lawyers contend that Comey damaged his credibility as a witness during his book tour this spring by showing that he played by his own rules when he ran the FBI, and that the findings of a recent inspector general report critical of the FBI’s handling of the Hillary Clinton e-mail investigation buttressed their case.

Giuliani views the tactics as an early success. “Right now, public opinion is going in our direction big time,” he said.

His approach also extends to his public portrayal of the negotiations with Mueller over a presidential interview. Even as they have delayed any agreement for at least six months of negotiations, the lawyers have condemned the special counsel for dragging out the inquiry, saying he has had more than enough time to complete his investigation.

Giuliani has gone back and forth about whether the president will agree to be questioned and given varying timetables. He once said Trump would make a decision after his meeting with the North Korean leader, Kim Jong Un, last month, then changed that deadline to July. The president’s lawyers have set other deadlines that came and went without resolution.

This stalling has all but dared Mueller to subpoena Trump to testify, potentially setting off a monthslong battle in court about whether the president can be compelled to answer questions under oath.

Also prompting a shift in the president’s strategy was the conclusion by his lawyers that even if Mueller finds evidence of wrongdoing, he will adhere to Justice Department memos that say the president should not be indicted, and is likely to instead send a damaging report on Trump’s conduct to Congress.

Critics see the array of delay tactics as aimed at stalling an investigative report to Congress until after November’s midterm elections. The more time Trump and his lawyers have to influence Americans’ views of the inquiry, the better their chances to undermine its credibility and pressure lawmakers not to impeach Trump.

Legal experts are skeptical that the new tactics will be effective. “It’s a gambit because if there’s damaging information that comes out down the line — like primary source documents or testimony — then you’ve spent your capital trying to create a public narrative that is belied by hard evidence,” said Stephen I. Vladeck, a professor at the University of Texas School of Law and an expert on constitutional law.

Dowd said the public did not appreciate the damage the investigation had done to both Trump and the presidency over the past year. He said he had come around to Trump’s view, first voiced by the president last summer, that Mueller is acting in bad faith.

“That’s the way the president was at the beginning,” Dowd said, “and the president was right.”