A member of the president’s legal team on Thursday strongly defended the “disciplined” way President Trump has handled his job and personnel contacts amid a probe by special counsel Robert Mueller.

The New York Times reported on conversations about the investigation Mr. Trump had with two witnesses, White House Counsel Donald McGahn and former Chief of Staff Reince Priebus. Mr. Mueller is investigating Trump-Russia contacts and reviewing whether there was obstruction of justice in Mr. Trump’s firing last May of FBI Director James B. Comey.

John M. Dowd, one of three lawyers on Mr. Trump’s team, told The Washington Times that the White House has gone to great lengths to cooperate with a special counsel. His appointment by Deputy Attorney General Rod Rosenstein blindsided the president.

“Truth is the president has been remarkably disciplined, respectful and supportive of the efforts of the special counsel even though the deputy attorney general appointed the special counsel without notice to the attorney general or the president,” Mr. Dowd told The Times. “No president in history has been more cooperative or transparent with special counsel.”

Mr. Rosenstein appointed Mr. Mueller after Attorney General Jeff Sessions recused himself from the Russia election interference probe. The recusal angered Mr. Trump, who second-guessed his decision to nominate Mr. Sessions.

The attorney general withdrew because he worked on the campaign as national security adviser and had met with then-Russian Ambassador Sergey Kislyak.

The conversation with Mr. McGahn involved the president asking him to publicly deny he wanted to fire Mr. Mueller, which the counsel refused, The New York Times said.

The Trump campaign and White House have turned over thousands of pages of emails and memos to Mr. Mueller. They have also made a number of staff available for interviews, including Mr. McGahn and his lawyers.

“These documents have been voluntarily provided by the president to the special counsel and the congressional committees and include privilege material of all kinds,” the lawyers say in a scorecard obtained by The Times. “The cooperation and transparency are unprecedented.”

The score card says the campaign provided 1.4 million pages of documents to Mr. Mueller’s team, including search terms and a comprehensive log.