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.
The statement implies that there is a possible internal investigation about conversations between President Donald Trump and Comey, but it wasn't clarified.
Comey also claimed he was anxious that Trump was trying to pressure him to drop the FBI's Russian Federation investigation.
Trump's tweets came after the top lawyer for his transition team warned the organization's officials to preserve all records and other materials related to the Russian Federation probe.
Mr Trump is unlikely to face criminal prosecution as a sitting president, but obstruction of justice could be grounds for impeachment.
In a report published on Wednesday, the paper quoted five people briefed on the requests, saying those who agreed to be interviewed include national intelligence director Daniel Coats, Admiral Mike Rogers who heads the National Security Agency (NSA), and his recently departed deputy, Richard Ledgett. He wrote in multiple social media posts that he views Mueller - a long-serving former Federal Bureau of Investigation director respected by both parties - as leading a biased probe with the singular aim of dislodging Trump.
The case for obstruction of justice isn't Comey versus Trump.
The memo that the White House at first said was critical to the decision, before Trump suggested it was irrelevant because his mind was already made up.
Moscow has denied USA intelligence agencies' conclusion that it interfered in last year's election campaign to try to tilt the vote in Mr Trump's favour.
"It is my view that fully investigating the facts, circumstances, and rationale for Mr. Comey's removal will provide us the opportunity to do that on a cooperative, bipartisan basis", Grassley said. But he had said last week he felt vindicated by Comey's testimony on June 8 that he was not the subject of investigation while Comey was heading the agency.
Vice President Mike Pence on Thursday hired his own lawyer to represent him in the special counsel's Russian Federation investigation. According to the 8-page lawsuit, Wallace's appeal of the FBI's initial denial for expedited processing argued that there "is a "great urgency" in release of the Comey memos 'which pertain [ ] directly to possible questions about the government's integrity affecting public confidence in the Presidency and the Executive Branch".
Mr Comey told a Senate panel last week he believed Mr Trump fired him to undermine the FBI's Russian Federation probe and testified that the President directed him in February to drop an investigation into former national security adviser Michael Flynn in relation to the Russian Federation matter.
At a Senate Intelligence Committee hearing last week, Coats and Rogers refused to say whether Trump asked them to intervene in the investigation, which is also examining whether the Trump campaign team colluded with Russian Federation during last year's presidential campaign.
Adam Schiff, the top Democrat on the House intelligence committee, would not comment on whether Mueller was looking at possible obstruction of justice by Trump but said Congress "certainly needs to get to the bottom" of the issue. What is clear is that he could order the Justice Department to ax Mueller, which may result in Rosenstein's departure and would certainly intensify the uproar over the investigation.