Deputy Attorney General Rod Rosenstein, who appointed Mueller last month, testified Tuesday he has seen no evidence of good cause to fire Mueller.
Trump's tweet seems to suggest he acknowledges that he is under investigation for obstruction of justice.
President Donald Trump made a surprising comment about the possible investigation into obstruction of justice for firing former FBI Director James Comey.
Citing "US sources familiar with the matter", The Washington Post reported Thursday that the business dealings of additional former members of Trump's team, including his campaign's chairman, Paul Manafort, ousted security adviser Michael Flynn and ex-security adviser Carter Page, have also come under scrutiny.
Trump published a series of tweets in which he decried both the alleged investigation and media coverage thereof.
The Post reported that the obstruction of justice investigation of the president began days after James Comey was sacked as the FBI Director on May 9.
Mueller briefed senators on his work on Wednesday.
President Donald Trump speaks in the Roosevelt Room of the White House in Washington, Thursday, June 15, 2017, during an event on Apprenticeship and Workforce of Tomorrow initiatives.
But Mr Comey also testified that to his knowledge the president had not tried to stop the Russian Federation investigation. Kushner was also already under investigation for his secret meetings with several key Russian players, including Russian ambassador Sergey Kislyak and Russian banker and Putin spy Sergey Gorgov.
Bill Cosby trial: Accuser says she was 'frozen' after being drugged
Cosby, who denies all the charges, says he gave Ms Constand an antihistamine tablet and that the sexual encounter was consensual. Today , in a Pennsylvania courtroom, she told her story publicly for the first time. "And so, I just went along with it".
Even if Trump is indicted, it will not amount to much legally unless Congress - where Republicans have a majority - steps in to impeach him.
The White House has denied any collusion, and Trump has repeatedly complained about the probe, saying Democrats can not accept his election win.
In May, Trump fired Comey, saying "this Russian Federation thing" was on his mind when he made the decision to oust the nation's top law enforcement official while Comey was leading the FBI's probe into Russia's meddling.
According to the news accounts, neither Coats nor Rogers complied with Trump's requests.
Americans are mixed on whether Mueller can lead a fair and impartial investigation.
After Comey's firing, the administration gave differing reasons for his dismissal. Mr Trump later contradicted his own staff, saying on 11 May he had the Russian Federation issue in mind when he fired Mr Comey.
The leaders of the Senate Intelligence committee said in a statement issued Wednesday that they "look forward to future engagements" with Robert Mueller.
Kasowitz said on Wednesday that leaking Federal Bureau of Investigation information about the president was "outrageous, inexcusable and illegal", although he did not question the content of the article. At the time of that report it was not clear that the FBI was investigating Kushner's business dealings. "It is my view that fully investigating the facts, circumstances and rationale for Mr Comey's removal will provide us the opportunity to do that on a cooperative, bipartisan basis", the letter said.
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