The tweets are the latest in a week of angry social media responses by the President over a report by the Washington Post that Mr Mueller was looking into whether he had obstructed justice. The Wall Street Journal reported that it was Trump's firing of Comey that is "now a subject of the federal probe ... which has expanded to include whether the president obstructed justice".
Comey testified under oath to Congress last week that he believed he was sacked 'because of the Russian Federation investigation'.
Comey also testified he had told Trump he was not under investigation.
When The Washington Post reported this week that Mueller was investigating Trump for obstruction of justice, a spokesman for the President's private attorney called the leak "outrageous, inexcusable and illegal". All three men have agreed to be interviewed, the source said.
The obstruction of justice investigation into Mr Trump began days after Mr Comey was sacked on May 9, according to people familiar with the matter, the Washington Post said.More news: Warriors Green makes fun of Cavaliers
The move by special counsel Robert S. Mueller III to investigate Trump's conduct 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.
Robert Mueller, the special counsel named by the department to investigate the Russian Federation matter, is now examining whether Trump or others sought to obstruct the probe, a person familiar with the inquiry said on Thursday. "I can go around them".
A spokesman for Mr Mueller's team declined to comment on Wednesday.
Rosenstein did not explain why he issued the statement.
Senate Intelligence Committee Chairman Richard Burr, R-N.C., and Sen. An aide familiar with the meeting said it was held to discuss the investigations, including ways that the parallel inquiries don't interfere with one another.More news: Amazon buying Whole Foods, road closures, Judge David Lewis
It was a memo written by Rosenstein that was originally used by the White House as justification for Comey's firing. That investigation is being overseen by Robert Mueller, who was appointed as a special counsel last month.
United States president Donald Trump has appeared to confirm he is under investigation for his dealings with Russian Federation and for firing former FBI directer James Comey. "Sad!" the U.S. president tweeted.
ABC said Rosenstein told Associate Attorney General Rachel Brand she would have authority over the probe if he were to step aside.
"You and I agree that the American people deserve a full accounting of attempts to meddle in both our democratic processes and the impartial administration of justice".
Feinstein has said the Judiciary Committee should investigate, but had asked Grassley to keep the investigations separate.More news: McIlroy trying to make up ground at US Open
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