A person who has spoken to Trump within the last 24 hours told CNN "the man" in the tweet is Rosenstein, who wrote a memo recommending Comey's firing and approved the appointment of a special counsel to look into Russian election meddling.
Comey told the U.S. on live TV that there was no doubt the Russians interfered in last year's election.
But Mr Comey also testified that, to his knowledge, the president had not tried to stop the Russian Federation investigation.
Recent news reports have suggested Trump sought all three officials' help in pressuring FBI Director James Comey to drop his investigation into former National Security Adviser Mike Flynn.
Trump's tweets are the latest - and most direct - attacks on the leader of an investigation that he insists is unnecessary and distracting. I don't know whether the Federal Bureau of Investigation and Mueller's crack team of prosecutors have any solid evidence of collusion or shady financial deals. The New York Times also reported the story.
The White House has said the president "has never asked Mr Comey or anyone else to end any investigation, including any investigation involving General Flynn".
"Americans should exercise caution before accepting as true any stories attributed to anonymous 'officials, ' particularly when they do not identify the country ― let alone the branch or agency of government ― with which the alleged sources supposedly are affiliated", Rosenstein said. Richard Burr, R-N.C., right, chairman of the Senate Select Committee on Intelligence, and Vice Chairman Mark Warner, D-Va., left, listen as Attorney General Jeff Sessions testifies before the Senate Select Committee. An aide familiar with the meeting said it was held to discuss the investigations, including ways that the parallel inquiries don't interfere with or overlap one another.More news: RSA Insurance Group Plc (RSNAY) Reviewed By Analysts
The memo sent Thursday asks for records related to foreign travel, contacts with Russian "officials, agents or nationals" and background investigations into the top Trump associates now targeted by Mueller's probe.
After the firestorm caused by Comey's firing, Rosenstein appointed Mueller, Comey's predecessor as FBI director, to take over the DOJ Russia investigation. Dianne Feinstein, the top Democrat on the Senate Judiciary Committee, in a statement.
Grassley announced the investigation in a letter to California Sen.
"The FBI leak of information regarding the president is outrageous, inexcusable and illegal", said Mark Corallo, the spokesman, according to the Post.
"You and I agree that the American people deserve a full accounting of attempts to meddle in both our democratic processes and the impartial administration of justice ..."
Mueller's friendship with Comey and Mueller's selection of several investigators who have made campaign donations to Democrats are among the issues Gingrich is raising as problematic.
Mueller also has expansive powers to investigate any matters that develop from his initial investigation. The President has stressed he was not under investigation, and has taken to Twitter to dismiss the entire investigation as a hoax.