Sessions' testimony came in the wake of fired FBI Director Comey's assertion that he believed he was sacked by Trump as part of an effort to influence the agencies' investigation into Russia's meddling in the presidential polls.
Although Rosenstein is the lead justice department official in the case (after attorney general Jeff Sessions recused himself because he is himself under the lens for Russian Federation contacts), the legal rationale he cited for the Comey firing was his sloppy handling of the Hillary email server case.
Mr Rosenstein has been overseeing the Russian Federation probe since shortly after attorney general Jeff Sessions recused himself.
U.S. President Donald Trump is being investigated by special counsel Robert Mueller for possible obstruction of justice, the Washington Post reported on Wednesday, citing unidentified officials.
Several US congressional committees are also looking into the question of Russian election interference and possible Trump campaign collusion.
Even if Mueller's probe finds evidence Trump tried to obstruct justice, the Justice Department - which oversees the FBI and the special counsel investigation - is highly unlikely to indict a sitting president.
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.
Mr Comey told Congress last week that before being sacked, Mr Trump pressured him to drop an investigation into his former national security adviser, Mike Flynn, who was forced to quit for lying about his links to Moscow. "Sad!" the US President tweeted. Earlier tonight the Post reported Vice President Mike Pence has retained private counsel to help him in the Russian Federation probe.
Mueller has been building a team of investigators for a wide-ranging inquiry into Russia's meddling. Meanwhile, former House Speaker Newt Gingrich slammed Mueller for reportedly launching investigation against Trump.
Rosenstein's selection of Mueller puts the probe in the special counsel's hands, but it would still fall to Rosenstein to make decisions about resources, staffing and, ultimately, prosecutions, ABC News pointed out.
Earlier on Thursday, Trump called the probe a "witch hunt" on Twitter.
Trump's Twitter response followed days of intensifying criticism of Mueller from some conservatives who have charged the former Federal Bureau of Investigation director and his team with political bias and have claimed his relationship to Comey and an earlier meeting with Trump amount to conflicts of interest.
Trump's personal attorney, Marc Kasowitz, responded to this report evading responsibility and blaming leakers.
Senator Dianne Feinstein, the top Democrat on the Senate judiciary committee, said she was "increasingly concerned" that Trump will fire both Mueller and Rosenstein.
"The FBI's leak of information regarding the president is outrageous, inexcusable and illegal, " said Mark Corallo, spokesman for Trump's outside legal team.
Trump also criticized the change in focus of the investigation on Thursday, saying that it was run by "some very bad and conflicted people!"
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