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Both men spoke out as special counsel Robert Mueller continues to probe alleged collusion between Team Trump and Russian Federation ahead of the 2016 presidential election.

In several Monday morning tweets, Trump reasserted his lawyer's claims and continued to take aim at the investigation, calling it a "witch hunt" and "unconstitutional".

Giuliani's statements arrive one day after The New York Times discovered that Trump's lawyers argued the following notion to special counsel Robert Mueller: Trump couldn't possibly obstruct justice, ever, because he can shut any investigation down, at anytime, anyway.

In an interview with the Huffington Post on Sunday, Giuliani said that "in no case" can the president be subpoenaed or indicted, even if he committed murder.

His comments echoed Giuliani's, who said Sunday that a self-pardon was out of the cards and could lead to impeachment - but Trump could do it if he wanted to.

Does President Trump have the power to pardon himself?

Many legal experts say the President's actions could be considered obstruction if prosecutors can show he acted with "corrupt intent".

In another tweet he called Mr Mueller's appointment "totally UNCONSTITUTIONAL".

Nevertheless, Trump's lawyers are "trying to come up with a narrow group of conditions in which" Trump could testify before Mueller's team, "if we can justify the fact that they have an open mind and that they'll conclude the investigation".

The president's power to issue pardons is spelled out in Article II of the Constitution. He [has] no intention of pardoning of himself.

"If the president were to pardon himself, he'll get impeached".

The lawyers claimed in the January letter that President Donald Trump did in fact dictate his son's misleading statement to the New York Times in July of previous year regarding a campaign-era meeting with Russians promising dirt on Hillary Clinton. "And he has no need to do it; he's done nothing wrong".

"As only one of two people left who could become president, why wouldn't the Federal Bureau of Investigation or Department of "Justice" have told me that they were secretly investigating Paul Manafort (on charges that were 10 years old and had been previously dropped) during my campaign?"

Mueller's investigation has thus far failed to find any evidence of collusion or obstruction, but Trump will likely have to "play the game", for the rest of the summer.

Arguing for the points made in the memo, George Washington University law professor John Banzhaf said the Constitution suggests the only remedy for presidential wrongdoing is impeachment, the Washington Examiner reports.