It was confirmed by the White House that Mueller was among the candidates who Trump interviewed to replace Comey. While the investigation had originally been focused on potential collusion between the Trump campaign and Russian Federation, the Post reported, the obstruction inquiry began after Trump fired Comey.
A source on Trump's legal team attempted to clarify the missive, claiming he was reacting to media reports about the investigation rather than offering public confirmation.
The Trump tweets come after the top lawyer for his transition team warned organization officials to preserve all records and other materials related to the Russian Federation probe. "The Department of Justice has a long-established policy to neither confirm nor deny such allegations".
The President's tweet sparked immediate speculation about the future of the official, Rod Rosenstein, who wrote a memo recommending Comey be ousted and also later approved the appointment of a special counsel - Robert Mueller - to lead the Russian Federation probe.
Robert Mueller, the man chosen to take over the inquest as special investigator, had started investigating into president Trump's behaviour.
Mr. Rosenstein took over the investigation into whether Russian Federation tried to tip the U.S election in favour of Mr. Trump after Attorney General Jeff Sessions recused himself in March.
The transition official said the organization has also separately asked the General Services Administration to preserve records from the Trump transition that were transferred to its facilities after Trump's inauguration.
California Sen. Dianne Feinstein said she is concerned that Trump might try to fire both Rosenstein and Mueller.
Comey said he believed Trump's advice to be a direction and thus felt uncomfortable by it.
Flynn, who was forced out in February, is a subject in investigations by intelligence committees in the House and Senate, as well as the Federal Bureau of Investigation.
The memo from the transition's general counsel directs all staffers and volunteers who worked on the Trump transition to "preserve any written documents.as well as any electronic information" related to Russia, Ukraine and any foreign travel by Trump transition members.
The interest in Kushner's activities by the special counsel's office is no more extensive than the FBI's interest in his multiple roles on both the Trump campaign and transition team, which CNN reported last month.
A representative for Trump's lawyer promptly reacted to the allegation.
Trump also lashed out at the media, on a day that aides hoped would be focused on his decision to undo some of Barack Obama's detente with Cuba. A spokesman for Trump's personal attorney had strong words in response to the news. Trump has repeatedly complained about the probe, saying Democrats can not accept his election win.