Mueller's friendship with Comey and Mueller's selection of several investigators who have made campaign donations to Democrats are among the issues Gingrich is raising as problematic.
The Washington Post this week reported, not only that the president is under investigation for possible obstruction of justice, but also that the FBI inquiry is examining the business and financial dealings of the president's son-in-law Jared Kushner. "Mueller is setting up a dragnet of obstruction, financial questions and every aspect of Trump's life and his associates lives.very risky", Gingrich said.
On Twitter, Mr Trump dismissed as "phony" the idea his campaign colluded with any Russian effort to sway the 2016 United States election.
Burr said there's a reason for the committee's interest in interviewing these senior intelligence officials: To determine whether there was any collusion between Russian officials and Trump associates, a sign that obstruction was not part of his panel's purview. "Nice", Trump wrote in his first tweet.
If true, the investigation represents an expansion of Mr Mueller's original probe into links between Moscow and the 2016 Trump presidential election campaign.More news: Jared Kushner speaks at tech event
The White House confirmed Mr Mueller was among the candidates the president interviewed to replace Mr Comey.
Shortly thereafter, he followed that up with another tweet, in which he returned to one of his main themes regarding the ongoing probe: "You are witnessing the single greatest witch hunt in American political history - led by some very bad and conflicted people". Trump tweets. Echoing tweets from Thursday, he concludes by adding: "Witch Hunt".
Trump aides have urged him to stop meddling in the investigative process, but law enforcement and intelligence officials have recounted how the president has asked them to push back against the probe or to publicly exonerate him.
Mr Comey, who was sacked on May 9, told the Senate Intelligence Committee last week he believed President Trump dismissed him to undermine the FBI's Russian Federation probe.
Mr. Mueller's investigation appeared to be reaching a circle of current and former officials.
Trump had expressed the same outrage when Mueller, a former Federal Bureau of Investigation director from 2001 to 2013, was appointed last month by the US Department of Justice to probe Russian meddling. Last week, Comey testified in a Senate hearing that he believed he was sacked "because of the Russian Federation investigation".