Hours after Mr Trump's tweet, a source close to his outside legal team said the President did not intend his tweet to be confirmation of the investigation but rather was a reaction to a Washington Post story about the probe from Wednesday (local time).
After Comey's firing, Rosenstein appointed Mueller to lead an independent investigation on matters involving Russia's alleged meddling and related matters. In the same interview the President suggested that he was thinking about the Russian Federation investigation at the time he terminated Comey.
"I've talked with Director Mueller about this", Rosenstein told AP. The Democrats like him.
Others felt Trump was on the right track.
In an early-morning tweetstorm, Trump blasted the investigation as a "witch hunt" and a "phony story".
"I will say candidly the president and federal government generally, I think, would be better off generally with fewer tweets", said Sen. "He sits in the Oval Office".
However, it is likely that he was tweeting about Deputy Attorney General Rod Rosenstein, or Mueller who is examining whether the president obstructed justice by firing ex-FBI Director James Comey last month amid the ongoing Russian Federation investigation.
Mr Trump, who is due to give a speech in Miami on Friday where he is expected to announce a shift in U.S. policy towards Cuba, also boasted about his deployment of social media, despite warnings by legal experts that his tweets may be used against him in the ongoing investigation. Naturally, he condemns it as a "witch hunt".
"They clearly don't have control over what he's tweeting and it has been long standing practice that when you're under investigation you don't attack publicly the investigators".
The White House confirmed that Mueller was among the candidates Trump interviewed to replace Comey.
Trump's surrogates have launched a broad campaign to discredit Mueller, claiming conflicts of interest and that he has been bringing on prosecutors who have supported Barack Obama and Hillary Clinton. Allies have even floated the idea that Mueller may be fired.
Was the Rosenstein memo the reason Comey was sacked? But Trump apparently wants to keep the option open. But Rosenstein, too, may ultimately have to hand off oversight given his role in Trump's decision to fire Comey.