The President's tweet - seeming to confirm the probe based on news reports - came as a surprise to the President's own legal team, according to a person briefed on the matter. The tweet was not confirmation that the president or his attorney has been informed by the Department of Justice or Mueller that Trump is the subject of an investigation.
In recent days, there have been major rumors that the president was thinking about firing Mueller.
Trump's Twitter response followed days of intensifying criticism of Mueller from some conservatives who have charged the former Federal Bureau of Investigation director and his team with political bias and have claimed his relationship to Comey and an earlier meeting with Trump amount to conflicts of interest.
Trump fired Comey on May 9, citing recommendations made to him by Rosenstein.
It was not clear whether the president was basing his tweet on direct knowledge, or on reports this week that special counsel Robert Mueller is examining whether he obstructed justice by firing Mr Comey last month amid the Russian Federation investigation. Investigators have also been looking for any evidence of possible financial crimes among Trump associates, officials said. The order also demands that records be kept on any foreign travel by members of Trump's transition team and presidential campaign.
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Canning Rosenstein would thrust Brand into the captain's chair of the Russian Federation probe, at least until the Senate confirmed a new deputy attorney general.
The recusal question has surfaced before, amid speculation Rosenstein could become part of the Robert Mueller probe given his role in the firing of former FBI Director James Comey.
Trump demonstrated Friday morning that the Russian Federation probe continues to consume his attention, tweeting a stream of messages decrying the controversy.
President Donald Trump has appeared to acknowledge he is under investigation in the inquiry into alleged Russian meddling in the U.S. election.
Rosenstein told the Associated Press earlier this month that when he hired Mueller he discussed the possibility of having recuse himself "if anything that I did winds up being relevant to his investigation" and if recusal is necessary.
On Thursday, Trump blasted news reports that he is under criminal investigation as a "witch hunt" against him led by some "very bad" people.
Mr Trump was not under investigation before Mr Comey's firing, but reportedly is now facing scrutiny for obstruction of justice over the circumstances surrounding the ex-FBI chief's sacking, according to United States media.