Trump's tweets prompted Sen.
Comey told a Senate panel last week he believed Trump dismissed him to undermine the FBI's Russian Federation probe.
Citing unidentified sources, the news station reported that Rosenstein told Brand she would be tasked with the final decisions regarding resources made available for the probe, headed by special counsel and former FBI director Robert Mueller, and whether anyone is prosecuted because of the investigation.
"As you and I have discussed, however, I can not defend the Director's handling of the conclusion of the investigation of Secretary Clinton's emails, and I do not understand his refusal to accept the almost universal judgment that he was mistaken".
Mr Rosenstein played a part in the dismissal of former Federal Bureau of Investigation director James Comey who was sacked by Mr Trump in May.
Although the president is unlikely to be indicted if the Mueller's investigation finds any criminal wrongdoing, Mueller's findings could lead to calls for impeachment in Congress, where a few Democrats already are pushing for impeachment.
A few days after the March 22 meeting, Mr Trump spoke separately with Mr Coats and Mr Rogers and asked them to issue public statements to the effect that there was no evidence of coordination between his campaign and Russia, AFP reported. Dianne Feinstein (D-CA), who said she's anxious that the President will try to fire both Mueller and Rosenstein.
Trump slammed the development as political witch hunt.
The Post, less than a month ago, reported Kushner was under FBI "scrutiny" in the Russian Federation investigation.
Inside the White House, a sense of foreboding has taken hold on even the most junior staff and up to the Oval Office, as news emerged that Vice President Mike Pence has hired a high-powered outside counsel to represent him.
Trump took to Twitter, his favourite tool of communication, to lament the "witch hunt" against him and accuse Hillary Clinton of destroying evidence tying her to Russian Federation.
Rosenstein authored a memo that criticized former FBI Director James Comey over his handling of Hillary Clinton's emails.
And Gingrich's final tweet on Thursday: "The brazen redefinition of Mueller's task tells you how arrogant the deep state is and how confident it is it can get away with anything".