Reports have raised questions about whether Trump requested their help in trying to get James Comey, then the Federal Bureau of Investigation director, to end an inquiry into Trump's former national security adviser, Michael Flynn.
Former FBI Director details meetings with Trump.
If Mueller strays from the straight and narrow, Rosenstein should not hesitate to remove him and name someone else to serve as special counsel.
Sekulow responded: "I can't read minds".
Mr Trump was not under investigation before Mr Comey's firing, but reportedly is now facing scrutiny for obstruction of justice over the circumstances surrounding the ex-FBI chief's sacking, according to United States media.
The most important takeaway from the president's tweet, Gergen continued, "is that the president has launched a campaign to discredit the special counsel and to discredit the investigations".
They said previous presidents would make sure to have the White House counsel's office and their personal lawyers carefully review any comments about such an investigation before making them.
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However, Mr Comey has since suggested that Mr Trump attempted to get him to shut down the investigation into his sacked former National Security Adviser Michael Flynn. The president has directed some of his frustration at Deputy Attorney General Rod Rosenstein and Mueller.
The Post reported last week that Robert Mueller - the special counsel appointed to investigate Russian involvement in the 2016 presidential election - was looking into whether Trump obstructed justice. Rosenstein appointed Robert Mueller on May 17 as special counsel to head the inquiry into the Russian Federation matter. Trump fired FBI Director James Comey, sent out spokespeople and surrogates with a far-fetched cover story to explain the dismissal, and then told NBC's Lester Holt that the real reason for the firing was Comey's pursuit of the Russian Federation investigation.
She said "the president has embarked on an effort to undermine anyone with the ability to bring any misdeeds to light". What is clear is that he could order the Justice Department to ax Mueller, which may result in Rosenstein's departure and would certainly intensify the uproar over the investigation.
The newspaper reported on Wednesday that director of national intelligence Dan Coats, head of the National Security Agency Mike Rogers, and former deputy director at the NSA Richard Ledgett, had agreed to be interviewed by Mr Mueller's investigators as early as this week. "Witch Hunt", the president wrote in his tweet.
Other prominent Republicans expressed more support for the probe and defended the integrity of Mueller.
The FBI and Congress are both looking at whether Trump campaign officials colluded with the alleged Kremlin plot.
Rosenstein was among those who advised Sessions to recuse himself, according to officials briefed on the matter. He may actually be a witness in the investigation he is supposed to supervise and like Sessions will be compelled by legal ethics to assume a seat on the sidelines. Pence's office confirmed he had retained Richard Cullen, a former Virginia attorney general and USA attorney for the Eastern District of Virginia, to assist "in responding to inquiries" from Mueller.
In a separate interview Sunday on CNN's "State of the Union," Rubio said the investigation process also is "the best thing for America".