Earlier on Thursday, Mr Trump tweeted that a new report suggesting that special counsel Robert Mueller may investigate him for possible obstruction of justice after he fired FBI Director James Comey is a "phony story".
In a later tweet, the President once again called the Russian Federation investigation a "witch hunt" and called the people leading it "very bad", apparently a reference to Mueller and others at the Federal Bureau of Investigation. Trump said that the report is a "phony story".
James Comey testified under oath to Congress on 8 June, recalling a private conversation with Trump saying, "I hope you can see your way clear to letting this go, to letting Flynn go", writes The Guardian.
Comey was later sacked, with Trump acknowledging that the Russian investigation was on his mind when he chose to dismiss him.
Trump vehemently denies any collusion between himself or any of his associates and Russian Federation. He and his team are investigating whether the President tried to pressure them to shut down the Russian Federation investigation.
Deputy Attorney-General Rod Rosenstein submitted a widely circulated memo to the President last month raising concerns over Mr. Comey's performance, but Mr. Trump later asserted that he had already made the decision himself to fire Mr. Comey.
A short time later, Trump ramped up his criticism with a new tweet, calling the investigation a "witch hunt" and calling its leaders "bad and conflicted".
A spokesperson for NSA Director Admiral Mike Rogers said the "NSA will fully cooperate with the special counsel".
The obstruction-of-justice investigation of the president began after Comey was sacked on May 9. Obstruction of justice is a potentially impeachable offense.