But in April, Mr. Trump concluded that Mr. 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 Mr. Trump’s longtime personal lawyer Michael D. Cohen.
After the raid, Mr. Trump decided to double down on his more aggressive strategy, according to people close to him. He hired Mr. Giuliani to replace his lawyer John M. Dowd, who had convinced Mr. Trump of the value of the earlier, more cooperative approach. Mr. Giuliani immediately began a public relations assault on Mr. Mueller. Mr. 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.
Mr. Giuliani has sown doubt and confusion by pushing dubious theories about the case. He has made claims like accusing Mr. Mueller’s office, without evidence, of trying to frame Mr. Trump. Mr. Giuliani has also pushed unfounded theories, like an assertion that the F.B.I. implanted a spy in Mr. Trump’s campaign.
The president and his lawyers have also tried to undermine key witnesses like James B. Comey, the former F.B.I. director fired by Mr. 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 Mr. Trump and his lawyers contend that Mr. 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 F.B.I., and that the findings of a recent inspector general report critical of the F.B.I.’s handling of the Hillary Clinton email investigation buttressed their case.
Mr. 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 Mr. 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.