President Donald Trump said Monday he has "the absolute right" to pardon himself — but added that he has "done nothing wrong."

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The tweet followed The New York Times' publication of a confidential letter over the weekend, in which Trump's lawyers argued to special counsel Robert Mueller that the president's broad powers mean he could not have obstructed justice.

The 20-page letter also suggested that the president even wields the constitutional ability to exercise the pardon power in matters related to the special counsel's probe of the links between the Trump campaign and Russia.

The assertion that a U.S. president holds an "absolute" power to pardon himself was endorsed on Sunday by Rudy Giuliani, the former mayor of New York and a current member of Trump's legal team.

Read more: Trump lays out two rationales for pardoning himself in the Mueller probe

In an ABC News interview, Giuliani said Trump "probably does" have the power to pardon himself, though "he has no intention" of doing so.

In word and action, Trump's latest uses of the pardon power could hold implications for how the president plans to act as the Russia probe, and the numerous lawsuits it has spawned, move forward.

Trump exercised his power to pardon last week for a sixth time, for conservative author and filmmaker Dinesh D'Souza, who was convicted of making an illegal campaign contribution. In a tweet, Trump said D'Souza "was treated very unfairly by our government!"

Later that day, Trump told reporters he was considering pardoning celebrity lifestyle guru Martha Stewart and was considering commuting the sentence of ex-Gov. Rod Blagojevich of Illinois. He said both also had been treated "unfairly."

Stewart was convicted in 2004 and sentenced to five months for a conviction related to a stock-selling scheme. Blagojevich, a Democrat, was sentenced in 2011 to 14 years in prison on corruption convictions, including trying to trade the Senate seat that became vacant when President Barack Obama went to the White House. Stewart and Blagojevich had ties to Trump's "Celebrity Apprentice" reality TV show.

But Trump's latest tweets suggest he may be considering pardons for the very people who could be offering information about him to federal investigators.

In just over a year, the special counsel has issued more than a dozen indictments, against Russians accused of working to affect the 2016 election as well as former Trump campaign officials, such as former campaign chief Paul Manafort.

Mueller's team has also secured guilty pleas from Trump's first national security advisor, Michael Flynn, and Manafort's longtime associate, Rick Gates, among others. Both men have agreed to fully cooperate with the probe.

No president has ever pardoned themselves. But a Justice Department memorandum from 1974 — shortly before the resignation of President Richard Nixon — asserted that the president did not possess such a power.

"Under the fundamental rule that no one may be a judge in his own case, the President cannot pardon himself," Mary Lawton, former acting assistant attorney general for the Office of Legal Counsel, said in the memorandum.

Mark Osler, a former federal prosecutor who runs a commutations clinic at the University of St. Thomas, said the most controversial legal question is not the pardon itself, but what comes after.

"He can issue himself a pardon warrant. There is nothing to stop him from doing so," Osler said. "The question is what happens next. It could be that it could not be challenged until a prosecutor presented a charge against him, and he relied on the pardon as a defense."

Trump attacked the legal legitimacy of the special counsel in a follow-up tweet. Mueller's team, which was appointed by Deputy Attorney General Rod Rosenstein in May 2017, is "totally UNCONSTITUTIONAL," Trump said.

The president maintained in both tweets that he has done "nothing wrong."

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Numerous Trump campaign associates and other individuals have been interviewed as part of Mueller's investigation. While Trump has previously said he would like to participate in an interview, the letter argues that the special counsel must meet a high standard to prove that only the president himself could provide the information they seek.

The special counsel is also looking into whether an obstruction of justice occurred as part of the investigations into Russian meddling and possible collusion with the Trump campaign.

But Trump's lawyers contend in the letter that the commander in chief "could neither constitutionally nor legally constitute obstruction because that would amount to him obstructing himself, and that he could, if he wished, terminate the inquiry, or even exercise his power to pardon if he so desired."

A spokesman for the special counsel declined to comment on Trump's tweets. The White House did not immediately respond to CNBC's request for comment.

--CNBC's Tucker Higgins contributed to this report.