In some of the longest exchanges with reporters during a week filled with explosive headlines, including news that Comey had penned a memo documenting the president asking him to stop investigating Flynn, Trump said he thought the decision to fire Comey would be bipartisan, said repeatedly there was "no collusion" between his campaign and Russian Federation, and attempted to spin it as a partisan distraction.
Trump fired James Comey as Federal Bureau of Investigation director last week.
Former FBI director Robert Mueller's appointment as special counsel has been welcomed by politicians from both sides.
Congressional investigators "will have to be very leery of crossing into Mr. Mueller's lane", he said.
"I would be very discouraged if somehow this new special prosecutor would preclude Jim Comey from testifying in public before our committee", he said.
Under pressure, Deputy Attorney General of the United States Rod J. Rosenstein announced Mueller's appointment yesterday. In addition to his investigatory and prosecutorial abilities with relation to the interference in the election, as set out by Rosenstein, Mueller is also granted the capacity to pursue crimes committed in the course of his probe.
In a series of early morning tweets, Trump complained that he was being singled out in a way Democrats had not been.
Graham also said Trump should honor the Justice Department's decision to appoint a special counsel to oversee the investigation.
"As I have stated many times, a thorough investigation will confirm what we already know - there was no collusion between my campaign and any foreign entity", Trump said in a statement released by the White House.
Mr Mueller's broad mandate gives him not only oversight of the Russian Federation probe, but also "any matters that arose or may arise directly from the investigation".
"I find it hard to subpoena records of somebody like Mr. Flynn who may be subject to a criminal investigation because he has a right not to incriminate himself", he said, referring to Trump's ousted national security adviser Michael Flynn.
"No, no. Next question", he said, speaking at a press conference with the Colombian president.