The argument, however, is not necessarily that the appointment of any special counsel would be unconstitutional, but rather that this one is, because of the broad investigative powers given to Mueller.
The president on Thursday pardoned conservative commentator and filmmaker Dinesh D'Souza, who pleaded guilty in 2014 to USA campaign finance law violations.
Mueller's investigation is moving forward nonetheless, and as it does courts may have to confront questions with minimal if any historical precedent.
"There's a reason they're untested".
The letter was a bold assertion of presidential power and another front on which Mr Trump's lawyers have argued that the President can't be subpoenaed in the ongoing investigation into Russian meddling in the 2016 election.
"One of the defenses that Rudy Giuliani has been talking about with the president himself is that complying with the Mueller investigation would take an enormous amount of the president's time", he said.
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Washington has called that unacceptable and demanded North Korea embark on full and verifiable denuclearization. Last week, Trump met with the highest ranking North Korean official in 18 years at the White House.
Chief among those was former Trump administration national security adviser Michael Flynn, who in December pleaded guilty to lying to the Federal Bureau of Investigation about his pre-inaugural contacts with Russian Federation ambassador Sergey Kislyak. In their letter, Trump's lawyers contested that account, but also argued that the president could not have been attempting to interfere in an investigation he was not aware was underway.
"It's a great slogan, but the law doesn't treat the president equal in all respects", Blackman said.
The lawyers also argued the subpoena would be "a considerable burden for the President and his Office", and that "having him testify demeans the Office of the President before the world". It is unclear how that fight, should the case reach that point, would play out.
He also said that presidents have given testimony and produced documents often enough that "such interactions. can scarcely be thought a novelty". They have been trying to sway Mueller away from seeking a subpoena to force Trump to testify before a grand jury. Such a move could theoretically end in a court defeat for Mueller, and would nearly certainly prolong the investigation. It concluded that Trump's actions were in keeping with the expansive powers of the presidency and could not constitute crimes. "Am I confident because I was in that campaign at a very intimate level?"
Former Manhattan U.S. Attorney Preet Bharara, fired by Trump a year ago along with numerous other federal prosecutors, said it would be "outrageous" for a sitting president to pardon himself and that doing so would represent "almost self-executing impeachment". He called it inexplicable why the president's legal team was making arguments that were focused on the wrong obstruction-of-justice statute.
House Republican Majority Leader Kevin McCarthy said on CNN on Sunday that no president should pardon himself.
The attorneys concluded their letter by informing Mueller that "we have advised the president that ... your inquiry thus far demonstrates that no obstruction of the Flynn investigation or Russian collusion investigation appears to have occurred".