They included media reports that Mr Trump discussed sensitive intelligence on the Islamic State militant group with Russia's foreign minister.
The recently sacked intelligence official has agreed to the hearing amid growing concern over President Trump's ties to Russian Federation and his involvement in the ongoing the investigation into former National Security advisor Michael Flynn.
"No. No. Next question", Mr Trump told a news conference in the White House, when asked if he "in any way, shape or form" ever urged Mr Comey to end the probe.
In an Oval Office meeting with senior Russian officials last week, Trump called Comey a "nut job" and said firing the intelligence chief had relieved "great pressure" on him, The New York Times reported.
A White House official told CNN in response that the report was "not true", while an unnamed attorney cited in the report said he did not believe White House Counsel Don McGahn would have allowed members of his legal team to research impeachment.
In a separate news report on Friday, the Washington Post claimed that a senior White House adviser was a person of significant interest in the investigation into possible ties between Trump's election campaign and Russian Federation.
As he departs for his first global trip as president, Donald Trump faces yet another damaging White House leak.
Despite calls for Trump's impeachment from some corners, Republicans are believed to still back the president, while the majority of Democrats have not yet joined calls for the U.S. president's ouster.
The Times report added to the impression given by Trump himself in a television interview last week in which he said the Russian Federation issue was a factor in firing Comey.
When he announced Mueller's appointment this week, Rosenstein said Mueller will have "all appropriate resources to conduct a thorough and complete investigation".
Before the latest reports, the White House had hoped to shift attention away from the political firestorm in Washington to foreign policy as well as the president's ambitious pro-business economic agenda in Congress.
"The investigation would have always continued, and obviously, the termination of Comey would not have ended it", he said, insisting "the real story is that our national security has been undermined by the leaking of private and highly classified conversations". Rosenstein said that though he was personally fond of Comey, "I thought it was appropriate to seek a new leader".
Mueller's former law firm, WilmerHale, represents Trump's son-in-law Jared Kushner, who met with a Russian bank executive in December, and the president's former campaign manager Paul Manafort, who is a subject of a federal investigation. But lawmakers at both congressional sessions expressed frustration that Rosenstein would say little in answer to their questions about his actions - or others' - before Comey's firing.
As The New York Times has reported, after numerous encounters with the administration, Comey felt he had to set the parameters of appropriate protocol very clearly. "This is a ridiculous statement for him to make", Pelosi said.
"With all of the illegal acts that took place in the Clinton campaign & Obama Administration, there was never a special counsel appointed!"