President Donald Trump’s lawyers do not know just how much the White House counsel, Don McGahn, told the special counsel’s investigators during months of interviews, a lapse that has contributed to a growing recognition that an early strategy of full cooperation with the inquiry was a potentially damaging mistake.

The president’s lawyers said on Sunday they were confident Mr McGahn had said nothing injurious to the president during the 30 hours of interviews. But Mr McGahn’s lawyer has offered only a limited accounting of what Mr McGahn told the investigators, according to two people close to the president.

That has prompted concern among Mr Trump’s advisers that Mr McGahn’s statements could help serve as a key component for a damning report by the special counsel, Robert Mueller, which the Justice Department could send to Congress, according to two people familiar with the discussions.

Mr Trump’s lawyers realised on Saturday they had not been provided a full accounting after The New York Times published an article describing Mr McGahn’s extensive cooperation with Mr Mueller’s office. After Mr McGahn was initially interviewed by the special counsel’s office in November, Mr Trump’s lawyers never asked for a complete description of what Mr McGahn had said, according to a person close to the president.

Mr McGahn’s lawyer, William A. Burck, gave the president’s lawyers a short overview of the interview but few details, and he did not inform them of what Mr McGahn said in subsequent interactions with the investigators, according to a person close to Mr Trump. Mr McGahn and Mr Burck feared that Mr Trump was setting up Mr McGahn to take the blame for any possible wrongdoing, so they embraced the opening to cooperate fully with Mr Mueller in an effort to demonstrate that Mr McGahn had done nothing wrong.

On Sunday, Mr Trump’s lead lawyer dealing with the special counsel, Rudy Giuliani, appeared to acknowledge that he had only a partial understanding of what Mr McGahn had revealed. Mr Giuliani said his knowledge was second-hand, given to him by a former Trump lawyer, John Dowd, who was one of the primary forces behind the initial strategy of full cooperation.

“I’ll use his words rather than mine, that McGahn was a strong witness for the president, so I don’t need to know much more about that,” Mr Giuliani said of Mr Dowd on NBC’s “Meet the Press.”

But Mr McGahn, who as White House counsel is not the president’s personal lawyer, has repeatedly made clear to the president that his role is as a protector of the presidency, not of Mr Trump personally.

Legal experts and former White House counsels said the president’s lawyers had been careless in not asking Mr McGahn what he had planned to tell Mr Mueller’s prosecutors. The experts said Mr Trump’s lawyers had the right to know the full extent of what Mr McGahn was going to say.

Robert F. Bauer, a White House counsel under President Barack Obama, said Mr McGahn’s lawyer may have taken the most prudent course for his client by not addressing “each and every detail about the questions that were specifically asked and the specific answers given.”

In its article, The Times said Mr McGahn had shared detailed accounts about the episodes at the heart of the investigation into whether Mr Trump obstructed justice in the Russia inquiry. Some of the episodes – like Mr Trump’s attempt to fire Mr Mueller last summer – would not have been revealed to investigators without Mr McGahn’s help.

The article set off a scramble on Saturday among Mr Trump’s lawyers and advisers. The president, sequestered at his private golf club in Bedminster, New Jersey, solicited opinions from a small group of advisers on the possible repercussions from the article. The president ordered Mr Giuliani to tell reporters that the article was wrong, but Mr Giuliani did not go that far in his television appearances.

The report by The Times also reignited a debate about whether Mr Trump had been given bad advice by his former lawyers Mr Dowd and Ty Cobb to allow full cooperation with Mr Mueller’s team, including by waiving attorney-client privilege. Mr Dowd and Mr Cobb believed the cooperation would help prove that the president had done nothing wrong and bring a swifter end to the investigation.

But the strategy “put Don McGahn in an impossible situation, because once you waive that privilege and you turn over all those documents, Don McGahn has no choice then but to go in and answer everything, every question they could ask him,” Chris Christie, a former US attorney and a close ally of Mr Trump, said on ABC News’ “This Week.”

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The Times reported that Mr McGahn, over at least three interviews, laid out how Mr Trump had tried to ensure control of the special counsel investigation. Mr McGahn gave a mix of damaging and favourable information about the president, but he said Mr Trump did not go beyond his legal authorities as president.

Although Mr Trump’s lawyers have little idea what Mr McGahn told investigators, they said on Saturday and Sunday that Mr McGahn had helped the president.

In an email to members of Mr Trump’s legal team and other associates, which was obtained by The Times, Mr Dowd said he had made the right choice in urging cooperation.

“We protected President by not asserting attorney-client privilege,” Mr Dowd wrote. He added that, had the lawyers forced the Mueller team to subpoena witnesses, they would have lost the ability to exert privilege over witnesses and documents.

Still, Mr Trump was rattled by The Times report, according to people familiar with his thinking. The president, who is said to be obsessed with the role John W. Dean, the White House counsel to President Richard M. Nixon, played as an informant during Watergate, was jolted by the notion that he did not know what Mr McGahn had shared.

Mr Trump lashed out about the report on Twitter, saying that The Times had falsely insinuated that Mr McGahn had “turned” on him.

Last fall, Mr McGahn believed he was being set up to be blamed for any wrongdoing by the president in part because of an article published in The Times in September, which described a conversation that a reporter had overheard between Mr Dowd and Mr Cobb.

In the conversation – which occurred over lunch at a table on the sidewalk outside the Washington steakhouse BLT – Mr Cobb discussed the White House’s production of documents to Mr Mueller’s office. Mr Cobb talked about how Mr McGahn was opposed to cooperation and had documents locked in his safe.

After the account of the lunch conversation was published, Mr McGahn became convinced that Mr Cobb believed he was hiding documents. Concerned that he would be blamed, he decided to try to demonstrate to Mr Mueller that he and other White House lawyers had done nothing wrong.

As Mr Trump’s lawyers have shifted to a more antagonistic approach towards Mr Mueller, it has seemed increasingly unlikely that Mr Trump will sit for a voluntary interview. On “Meet the Press,” Mr Giuliani repeated his fear of a “perjury trap.”

“It’s somebody’s version of the truth, not the truth,” Mr Giuliani said of any statements by the president in such an interview.

“Truth is truth,” the show’s host, Chuck Todd, answered.

“No, it isn’t truth,” Mr Giuliani replied. “Truth isn’t truth.”