The FBI probe, now in the hands of special counsel Robert Mueller, shifted its focus to allegations of obstruction in the days after Trump fired the agency's then-director James Comey on May 9.
The tweet from Trump, who has complained throughout the week of a "witch hunt" against him, appears to directly target Rosenstein for the first time, who this week said he wouldn't fire Mueller without good cause.
Attorney General Jeff Sessions is also under investigation as a member of the Trump campaign, leading Sessions to recuse himself from the case and allowing Rosenstein to appoint Mueller to head the investigation, reports Fox News.
In another sign the investigation is expanding, lawyers for the Trump transition team issued a memo Thursday instructing those who worked for the transition to preserve documents in anticipation that investigators will request those materials for the probe into Russian interference into last year's presidential election.
The new tweets are the latest in a week of angry social media responses from the president over a report by the Washington Post that Mr Mueller was looking into whether Mr Trump obstructed justice.
Earlier, Rosenstein had authored an extensive and publicly-released memorandum recommending former FBI-chief James Comey's firing.
The Washington Post this week reported, not only that the president is under investigation for possible obstruction of justice, but also that the FBI inquiry is examining the business and financial dealings of the president's son-in-law Jared Kushner.
Top Democrats warned Mr. Trump against a power grab on Friday.
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An official confirmed to Fox News that Trump was referring to Rosenstein in the statement.
U.S. intelligence agencies concluded in a report issued in January that Russian Federation interfered in the presidential race to try to help Trump win, in part by hacking and releasing emails damaging to Democratic candidate Hillary Clinton. The White House press office immediately pointed to Rosenstein's detailed memo as the justification for Comey's surprise termination.
That he would confirm he is under investigation came out of nowhere, this official said.
ABC said Mr Rosenstein told Associate Attorney-General Rachel Brand she would have authority over the probe if he were to step aside.
"The President was not confirming the investigation".
"I've talked with Director Mueller about this", Rosenstein told AP.
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.
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