Earlier this month, Rosenstein told The Associated Press he would recuse himself from overseeing Robert Mueller's investigation if his role in former FBI Director James Comey's firing becomes relevant to the inquiry.
Trump later said he had planned to fire Comey regardless of what recommendation he received from Rosenstein and Attorney General Jeff Sessions, who has recused himself from the Russian Federation investigation.
Reuters also cited an anonymous source close to Trump's outside legal team who said Trump was reacting to a Washington Post story about the probe, and didn't intend the tweet to confirm an investigation.
The investigation, the president added is being led by "very bad and conflicted people".
The President complained the probe was unfair and wondered why his defeated Democratic opponent was not getting the same scrutiny. Comey testified before the Senate intelligence committee he felt pressured by the White House to drop the investigation.
Comey said he believed Trump's advice to be a direction and thus felt uncomfortable by it.
The White House has repeatedly referred all questions about Russian Federation to the President's personal attorney.
It culminated in a tweet Friday from President Donald Trump.
"They made up a phony collusion with the Russians story, found zero proof, so now they go for obstruction of justice on the phony story".
A memorandum penned by Rosenstein was cited by the Trump White House as the inspiration for the May ouster of James Comey, then-director of the Federal Bureau of Investigation.