The investigation, the president added is being led by "very bad and conflicted people". He lashed out at a top Justice Department official overseeing the inquiry, reflecting his mounting frustration with the unrelenting controversy that has consumed his early presidency.
Rosenstein did not explain why he issued the statement.
The new allegations against Trump center on his own admission that he fired Comey because of the Russian Federation investigation, and suggestions he asked several top intelligence officials for their help altering the direction of the inquiry.
Sen. Dianne Feinstein, the top Democrat on the Senate Judiciary Committee, said she was "increasingly concerned" that Trump will fire both Mueller and Rosenstein.
"In fact, when I made a decision to just do it, I said to myself, I said, 'You know, this Russian Federation thing with Trump and Russian Federation is a made-up story, ' " Trump told Lester Holt. "That's undemocratic on its face and a blatant violation of the president's oath of office".
The widened Russian Federation probe could have far-reaching repercussions for Trump's presidency, transforming his closest aides into witnesses and sucking yet more political oxygen out of the West Wing.
Mr. Trump's morning tweets included what seemed like a jab at former FBI Director Robert Mueller, the new Special Counsel for the Russian Federation probe, as he said the investigation was being "led by some very bad and conflicted people!"
While FBI Director James Comey told President Trump on three separate occasions that he was not personally under investigation for colluding with Russians in the 2016 election, that's NOT necessarily the case anymore.
The tweets came shortly after Rosenstein issued his unusual statement that appeared to be warning about the accuracy of such reports. Americans should be skeptical about anonymous allegations. "The Department of Justice has a long-established policy to neither confirm nor deny such allegations", Rosenstein's full statement read.
The complaints Trump aired Thursday afternoon followed a pair of morning tweets.
A spokesman for Mueller's team declined to comment on Wednesday. What is clear is that he could order the Justice Department to ax Mueller, which may result in Rosenstein's departure and would certainly intensify the uproar over the investigation. However, he said Comey's removal after refusing to carry out the president's wishes is "a serious matter".
Mueller is investigating Russian interference in USA elections and possible Russian ties to the Trump campaign.
After the firestorm caused by Comey's firing, Rosenstein appointed Mueller, Comey's predecessor as FBI director, to take over the DOJ Russia investigation.
USA TODAY previously reported that the FBI was investigating Kushner for his contact with Russian officials, but there was no word at that time that his financial dealings were part of the probe.
The move ordered Thursday by the transition's general counsel cast a wide net on documents tied to the Russian Federation investigation as well as inquiries into the activities of Trump associates.
The two hour-long testimony saw Comey further informing that Trump had directed him to drop an Federal Bureau of Investigation probe against former national security adviser Michael Flynn.
The White House has directed questions to outside legal counsel, which has not responded.
On Thursday an aide to Vice President Mike Pence revealed he was hiring Richard Cullen - a veteran of the Iran-Contra investigation, Watergate and the 2000 vote recount in Florida - as a private lawyer. He said that as head of the executive branch of government, Trump has "prosecutorial discretion" to end an investigation. Cohen has worked for Trump since the mid-2000s and was active in the campaign. The House Intelligence Committee is conducting its own, parallel inquiry.