Trump's digital volley appeared to be trained at Deputy Attorney General Rod Rosenstein, who recommended the firing last month of James Comey - an nearly unprecedented move that could yet imperil Trump's presidency.
But Robert Mueller has been appointed special counsel to investigate Russian involvement in the 2016 presidential election and possible collusion with the Trump campaign.
And, as it turned out, the FBI had already launched its own obstruction investigation days after the firing - right after Trump went on NBC and himself linked Comey's firing to "this Russian Federation thing".
On Friday, former House Speaker Newt Gingrich said that Trump technically "cannot obstruct justice" because he is the president. The questions included whether he had confidence in Rosenstein, whether he plans to fire special counsel Robert Mueller and how he knows he's under investigation by the FBI.
Trump may be referring to Deputy Attorney General Rod Rosenstein, who in a memo to Trump raised concerns over Comey's performance.
Mr Pence's office confirmed he had retained Richard Cullen, a former Virginia attorney general and United States attorney for the Eastern District of Virginia, to assist "in responding to inquiries" from Mr Mueller.
"The President was not confirming the investigation".
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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.
The new allegations against Trump centre on his own admission that he fired Comey because of the Russian Federation investigation, and suggestions he asked several top intelligence officials for their help altering the direction of the inquiry.
After all, fired FBI Director James Comey pretty much telegraphed that during his congressional testimony last week.
Trump has been growing increasingly agitated with Rosenstein over the last day or two in private White House meetings and in conversations with friends, multiple people have told CNN.
PRESIDENT DONALD TRUMP: Oh, I was going to fire regardless of recommendation. Mueller has been choosing his own staff, tapping top legal minds from inside and outside the Justice Department.
The president has long vehemently denied any collusion with Moscow, either by himself or his associates.
Trump allies have been questioning whether Mueller can lead an unbiased probe, given that some members of his team have made campaign contributions to Democratic candidates.
Trump also attacked the media Friday morning. The order also covers separate inquiries into several key Trump associates including former National Security Adviser Michael Flynn, campaign adviser Paul Manafort, foreign policy aide Carter Page and outside adviser Roger Stone.