It concluded that Trump's actions were in keeping with the expansive powers of the presidency and could not constitute crimes.
Ultimately, Trump's lawyers argued that the president should not be compelled to sit for an interview to assist Mueller's effort, arguing that the White House provided full access to documents and interviews with other senior staff that was sufficient to answer Mueller's questions about Trump's actions.
"The President's prime function as the Chief Executive ought not be hampered by requests for interview. Having him testify demeans the Office of the President before the world," they wrote.
The arguments parallel those that the President's lawyers have pressed publicly for months, even as quiet negotiations over whether Trump might agree to sit voluntarily for an interview have continued.
They help underscore the legal battle now underway between the White House and the Special Counsel. Should Mueller seek to compel Trump's testimony with a subpoena, the arguments advanced in the letter could ultimately form the basis of a courtroom battle that would probably reach the US Supreme Court.
After former New York Mayor Rudy Giuliani replaced Dowd as Trump's chief lawyer in March, he reopened negotiations with Mueller about forestalling that kind of public battle through a voluntary interview. Giuliani, at first, expressed confidence that he could resolve the matter within weeks.
But the debate has dragged on and, more recently, Giuliani has expressed wariness over having his client sit for an interview and said he would only agree if the Special Counsel's office first turns over internal documents that shed light on the beginnings of the FBI's probe in 2016, before Mueller's appointment.
He told the Washington Post last week that Trump's lawyers are drafting a letter to Mueller laying out those terms and that Jane and Marty Raskin, a husband-and-wife team from Florida assisting Trump's defence, are in contact with Mueller's office three times a week.
Mueller's team has told the President's lawyers that they think they have the power to issue Trump a subpoena and compel his testimony, but they have not yet sought to go down that route.
"They may do a subpoena. The subpoena would then be contested. That would be going on for months," Giuliani said.
Sekulow noted the consistency of Trump's legal position while bemoaning the leaking of the internal document.
"We have maintained a consistent legal argument throughout the many months of this inquiry. Our legal team would not disclose internal communications with the office of Special Counsel. We continue to maintain cooperative relations with the office of Special Counsel," he said.
Likewise, in a tweet sent shortly before the New York Times story was posted online, Trump questioned whether Mueller's team might have been responsible for the leak. "Is the Special Counsel/Justice Department leaking my lawyers letters to the Fake News Media?" he asked.
A spokesman for the Special Counsel's office declined to comment.