President Trump also lambasted the main stream media for their reaction to McCabe's firing.
Dowd said Rosenstein should follow in the footsteps of Attorney General Jeff Sessions, who fired former Deputy FBI Director Andrew McCabe late Friday based on internal assessments that McCabe lacked candor on multiple occasions.
Brennan has repeatedly clashed with Trump since the former reality star and property mogul won the presidency in 2016.
Trump and McCabe's relationship has always been fraught.
"When the full extent of your venality, moral turpitude, and political corruption becomes known, you will take your rightful place as a disgraced demagogue in the dustbin of history", he wrote. "America will triumph over you", Brennan, who was Central Intelligence Agency head under President Barack Obama, tweeted.
Brennan served under former president Barack Obama from 2013 to 2017.
Trump had previously warned that any investigation into his family's finances would cross a "red line", and he was reportedly furious about Mueller's maneuver.
"And they can judge for themselves who is honorable and who is not", Comey tweeted.
Comey pushed back as well, tweeting: "Mr President, the American people will hear my story very soon".
Part of Mueller's probe is looking into whether President Trump was trying to obstruct justice by firing Comey.
As a congressional hearing days after Comey's dismissal, McCabe contradicted White House assertions that the Trump campaign investigation was one of the "smallest things" on the FBI's plate. Sessions, whose job status has for months appeared shaky under his own blistering criticism from Trump, risked inflaming the White House if he decided against firing McCabe.
But the McCabe and Comey situations are also somewhat different. How many lies? How many leaks? "Worse, his second-in-command just lost his pension after more than 20 years with the bureau, while Comey is about to cash in on a book and publicity tour potentially worth millions". In each, he asked about Mr. McCabe's wife, Jill, who ran a failed campaign as a Democrat for the Virginia State Senate.
He provided no details in his tweet Saturday.
The former deputy had risen to the portfolio of being the Director of Federal Bureau of Investigation in unusual circumstances to start with. Trump's successful push to get McCabe fired is also undeniably more personal in nature, given McCabe was ousted just 26 hours before he was to gain full retirement benefits.
The firing will only stoke the political fires around the Mueller investigation of Trump.
Mr McCabe suggested the move was part of the Trump administration's "war on the FBI".
McCabe commented on leaking information to a former Wall Street Journal reporter about the investigation of Hillary Clinton and the Clinton Foundation, saying he was authorized to "share" the information and did so with the knowledge of "the director", which would have been Comey at the time.
Comey's series of notes detailed interactions with Trump that Comey said unnerved him.
"Dowd just confirmed it by connecting the two events and saying that Rosenstein should shut down the Russian Federation investigation and "follow the brilliant and courageous example" of AG Sessions", he added.
Attorney General Jeff Sessions said he officially fired McCabe after receiving a report from the Inspector General, the findings from the FBI Office of Professional Responsibility and the recommendation of the Justice Department's senior career official.