"He was hired by Jeff Sessions", Trump said in an interview with "The Geraldo Show" on WTAM radio.
He added it's the responsibility of the media to report the facts, however comforting or discomforting they may be.
"Before the election, the people in question tried to taint the election, tip it to Clinton's favor; after the election, they're trying to undermine the president", Graham said.
"We believe our first duty is to this country, and the president continues to act in a manner that is detrimental to the health of our republic", the writer said.
Kavanaugh Denies Fresh Harassment Allegations From College Classmate
They also compared the current controversy to the sexual harassment allegations against Clarence Thomas by Anita Hill in 1991. Senator Chris Coons (D-Del), called Trump's comments "unacceptable and beneath the Presidency of the United States".
Both articles cite memos written at the time by Andrew McCabe, then the acting Federal Bureau of Investigation director, in which he noted Rosenstein discussing the 25th Amendment and wearing a wire.
But in Washington, more cautious voices warned of outcry on Capitol Hill if Trump moved to fire the man who oversees special counsel Robert Mueller's Russian Federation investigation. The White House did not respond to requests for comment.
"If Rosenstein is involved, he should be fired".
For months, there has been speculation that Mr. Trump could fire Mr. Sessions, Mr. Rosenstein or perhaps both.
The reported conversation about possibly secretly recording the president took place at a tense May 2017 meeting during the tumultuous period that followed Trump's firing of FBI Director James Comey. "But one thing that's clear: Whether you're a Republican or Democrat president, you have a right to a deputy attorney general that doesn't think you're incompetent and doesn't feel the need to audiotape conversations with you". At a rally in Missouri on Friday night, the president said there was a "lingering stench" at the Justice Department that "we're going to get rid of".
Rosenstein's alleged allusion to the 25th amendment of the US Constitution, which provides for removing a president if they are judged unfit for office, came just after Trump fired Federal Bureau of Investigation director James Comey - invoking a memo written by Rosenstein.