The Democratic National Committee called on Mr Rosenstein to recuse himself from the Russian Federation matter, but it said authority over the investigation should be given to Mr Mueller and not another Trump appointee. Trump had previously boasted that he was not personally under investigation, and Comey said the president had repeatedly pressured him to publicly clear him.
He appeared to be referring to Rod Rosenstein, deputy attorney general who is now leading the probe.
It's unclear why Rosenstein issued the warning or whether anyone prompted him to do so.
Trump's tweets prompted Sen.
Session himself has been under fire for his alleged secret communications with Russian officials as a surrogate for Trump during the 2016 US presidential elections. "That's undemocratic on its face and a blatant violation of the president's oath of office".
Kushner's attorney said such a review would be "standard practice". But Rosenstein, too, may ultimately have to hand off oversight of the probe given his own role in Comey's firing.
Trump "believes that he has the power to fire anyone in government he chooses and for any reason", said Representative Adam Schiff, whose committee is also investigating Russia-Trump ties.
Deputy attorney general Rod Rosenstein submitted a widely circulated memo to the president last month raising concerns over Mr Comey's performance, but Mr Trump later said he had already made the decision to fire Mr Comey.
A Justice official said Rosenstein was motivated in part because of frustration that recent news stories have unfairly brought on a torrent of "leak" accusations against the Federal Bureau of Investigation and Mueller's team.
A Department of Justice spokesperson declined to address what prompted the statement.
Intially, the Trump administration pointed to that memo to justify Comey's firing.
Several White House officials and Trump associates insisted on anonymity from the Associated Press in order to discuss the president's views of the unfolding investigation. Comey was sacked by the president on May 9 while he was overseeing the investigation into potential Russian interference into last year's election and potential collusion with the Trump presidential campaign. Rosenstein penned a letter outlining why he thought Comey could be let go, a letter the president reportedly asked him to write. "I don't think we have been formally told he's under investigation", the official said.
In another development, members of Trump's transition team that served him after he was elected in November until he took office in January have been ordered to preserve materials related to the Russian Federation matter, the New York Times reported.
In his statement, Comey said Trump asked him to drop the investigation into ties between former national security advisor Mike Flynn and Russian Federation.
Trump ignored shouted questions from reporters about the ongoing Russian Federation controversy as he departed the White House Friday for Miami. Pence headed the Trump transition until inauguration day.
Trump's personal attorney Michael Cohen has hired Washington, D.C. -based counsel.
Trump's surrogates have launched a broad campaign to discredit Mueller, claiming conflicts of interest and that he has been bringing on prosecutors who have supported Barack Obama and Hillary Clinton.
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