He also claimed that the person investigating him advised him to fire Comey, though it's unclear whom he was referring to.
He has questioned why investigators don't dig into the links between the Democrats and the Russian government, including his general election opponent, Hillary Clinton.
"As the deputy attorney general has said numerous times, if there comes a point when he needs to recuse, he will", Justice Department spokesman Ian Prior said in a statement. He lashed out at a top Justice Department official overseeing the inquiry, reflecting his mounting frustration with the unrelenting controversy that has consumed his early presidency.
According to ABC, "sources" stated that Rosenstein, the number two man at the Department of Justice, "has privately acknowledged to colleagues that he may have to recuse himself from the matter".
Comey, whom Trump fired in early May, said in Senate testimony earlier this month that the President spoke to him privately on February 14 and asked him to drop the bureau's investigation into former National Security Adviser Michael Flynn's alleged ties to Russian Federation.
Trump advisers and confidants describe the president as increasingly angry over the investigation, yelling at television sets in the White House carrying coverage and insisting he is the target of a conspiracy. Former FBI head Robert Mueller was appointed as special counsel a day after a report stemming from the notes was published.
Part of the revelations surrounding the Russian Federation investigation and the firing of Comey has been that Trump repeatedly pushed top intelligence officials to say in public that Trump was not personally under investigation and that there was no evidence of collusion between his campaign and Russian Federation in its interference in the 2016 election.
From 2011 until her confirmation, she was a lawyer for the US Chamber of Commerce business lobbying group's legal arm, which played a major role in marshalling legal opposition to environmental and labour regulations championed by Democratic former President Barack Obama. Pence's office confirmed he had retained Richard Cullen, a former Virginia attorney general and US attorney for the Eastern District of Virginia, to assist "in responding to inquiries" from Mueller.
Trump has called The Washington Post report a "phony story" and a "WITCH HUNT". Former [FBI] Director [Robert] Mueller has hired 13 lawyers.
Comey testified last week that he also felt pressured to drop the Flynn probe.
The memo sent Thursday asks for records related to foreign travel, contacts with Russian "officials, agents or nationals" and background investigations into the top Trump associates now targeted by Mueller's probe.
Though some in the White House have preached caution, fearing a repeat of the firestorm over Mr Comey's sacking, many in Mr Trump's orbit, including his son Donald Jr and adviser Newt Gingrich, have deemed Mr Mueller biased and worthy of dismissal.