While the Justice Department appointed Mueller to investigate Russian efforts to interfere in the 2016 presidential election - and any "collusion" with the Trump campaign - his assignment also includes "any matters that arose or may arise" from the Russia probe.
In another tweet, Trump wrote: "You are witnessing the greatest witch-hunt in American history, led by very bad and conflicted people!"
President Donald Trump's closest allies are attacking the integrity of those involved in the widening probe of Russian interference in the US election, accusing special counsel Robert Mueller of driving a biased investigation.
He tweeted early on Thursday morning, saying: "They made up a phony collusion with the Russians story, found zero proof, so now they go for obstruction of justice on the phony story".
The probe Mueller "marks a major turning point in the almost year-old FBI investigation, which until recently focused on Russian meddling during the presidential campaign and on whether there was any coordination between the Trump campaign and the Kremlin", The Washington Post reported yesterday.
CNN is suing the Justice Department for copies of fired FBI Director James Comey's personal memos on his interactions with President Donald Trump.
It also also heard from Attorney General Jeff Sessions about the Comey-Trump meeting and talked to several high-ranking officials about whether the president tried to interfere with the Russian Federation probe, CNN noted. Rosenstein had written a scathing memo criticizing Comey's handling of the Hillary Clinton email investigation, which the White House initially cited as the impetus for Comey's ouster.
The Senate judiciary committee does plan to investigate whether there was any interference with the FBI investigations, and the panel's chairman, Iowa Republican Chuck Grassley, has not ruled out investigating obstruction of justice as part of the probe.
Deputy Attorney General Rod Rosenstein appointed Mueller as special counsel shortly after Comey's firing.
Comey testified last week that he also felt pressured to drop the Flynn probe.
Speculation increasing that Trump will fire Special Counsel Robert Mueller
Gingrich less than a month ago had called Mueller a "superb choice: His reputation is impeccable for honesty and integrity". If President fired Bob Mueller, Congress would immediately re-establish independent counsel and appoint Bob Mueller .
File-This June 8, 2017, file photo shows former FBI Director James Comey speaking during a Senate Intelligence Committee hearing on Capitol Hill in Washington. Trump wrote on Twitter, in a pair of messages that ended with a reference to his campaign slogan "Make America Great Again".
Wallace said most lawyers would tell Trump to stop talking about the matter entirely following the report that Mueller is investigating Trump for obstruction of justice.
Interviews with the intelligence officials could happen before the week expires, according to the Washington Post.
Others have pointed to news that Mueller interviewed with Trump for the Federal Bureau of Investigation director post after Comey's firing. At the time of that report it was not clear that the FBI was investigating Kushner's business dealings.
But Mr Comey also testified that, to his knowledge, the president had not tried to stop the Russian Federation investigation.
Sessions, a close Trump adviser during the battle for the presidency, said in his opening statement that it was a "detestable and appalling lie" to suggest he was aware of or participated in any collusion between Russian Federation and the Trump campaign.
The tweets also are seen by some in the president's circle as the beginning of a case against the officials investigating him.
"Americans should exercise caution before accepting as true any stories attributed to anonymous 'officials, ' particularly when they do not identify the country - let alone the branch or agency of government - with which the alleged sources supposedly are affiliated", he said.
Mark Corallo, a spokesman for Trump's legal team, denounced the Post report, saying on Wednesday: "The FBI leak of information regarding the president is outrageous, inexcusable and illegal".
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