The White House clarification has come amidst reports that Trump is contemplating firing Mueller.
As attorney general, Sessions is unlikely to answer in detail questions about conversations he's had with Trump.
Multiple House Republicans said that there was no discussion about the special counsel at the weekly GOP meeting.
Karl Rove warns in WSJ oped today " special counsels can run amok".
Other Trump supporters homed in on the sequence of Mueller's job interviews.
U.S. President Donald Trump lashed out on Thursday after a report that he was under investigation into possible obstruction of justice, dismissing as "phony" the notion his campaign colluded with any Russian effort to sway the 2016 U.S. presidential election.
Last month, Gingrich praised Mueller's appointment, noting that the former Federal Bureau of Investigation director had an "impeccable" reputation for "honesty and integrity". Trump called because "I have been very clear" about Mueller and the lawyers he's hired amounting to a "rigged game", Gingrich said.
President Donald Trump has lashed out at the investigators driving the Russian Federation investigation as "very bad and conflicted people", responding angrily to reports that the special counsel is looking into whether Trump obstructed justice.
However, Adam Schiff, a Democrat member of the House Intelligence Committee Adam Schiff, said the House would not tolerate Trump firing Mueller.
The development comes a day after the daily reported that Mueller had extended his probe into determining whether the President tried to obstruct justice by suggesting to top intelligence and law enforcement officials that they end the Russian Federation investigation.More news: Play ball! GOP, Dems to battle as 1 - Team Scalise
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The president didn't clarify what exactly he was referring to in the early morning tweet, however he has frequently described reports about possible ties between members of his campaign and Russian Federation as a "witch hunt".
The friend, Christopher Ruddy, chief executive of Newsmax Media, who was at the White House Monday, said on PBS' "NewsHour" that Trump was "considering, perhaps, terminating the special counsel".
Justice Department spokesman Ian Prior declined to comment on the possibility of Trump seeking to remove Mueller.
Mr Ruddy appeared to be basing his remarks, at least in part, on comments from Jay Sekulow, a member of Mr Trump's legal team, who told ABC in an interview on Sunday that he was "not going to speculate" on whether Mr Trump might at some point order deputy attorney general Rod Rosenstein to sack Mr Mueller. Still, Gingrich said any special counsel with an agenda can "all of the sudden find something procedural and technical to latch onto".
On Monday, rumors that President Trump was considering firing Mr. Mueller set the Washington rumor mill into overdrive. If there were good cause, I would consider it, if there were not good cause, it wouldn't matter to me what anybody says.
Examining such possible charges will allow investigators to interview key administration figures including Attorney General Jeff Sessions, Rosenstein and possibly Trump himself, the source told Reuters. "I think he's weighing that option".
Barry Bennett, a GOP strategist who served as an adviser to Trump's campaign, said he believed it would be too damaging for Trump to try to remove Mueller, but that he had concerns about the appearance that the probe was being politicized.
But testifying in the Senate Tuesday, Rosenstein said he is confident that Mueller will have "the full independence he needs" to investigate thoroughly.
"I'm not going to follow any orders unless I believe those are proper and appropriate orders", he said. "I don't question his integrity at all, but he has to be careful not to create the impression of partiality".
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