The Senate Intelligence Committee, which has its own investigation of alleged Russian election interference, also wants Comey to appear in closed and open session.
Democrats have seized on the revelations about Trump in the aftermath of his firing of Comey.
On Tuesday, The Post and others reported that Comey kept detailed notes of his conversations with President Trump. Mr. Comey - who is 6 feet 8 inches tall and was wearing a dark blue suit that day - told Mr. Wittes that he tried to blend in with the blue curtains in the back of the room, in the hopes that Mr. Trump would not spot him and call him out.
"The president has the utmost respect for our law enforcement agencies, and all investigations", said the statement.
"While the president has repeatedly expressed his view that Gen. Flynn is a decent man who served and protected our country, the president has never asked Mr. Comey or anyone else to end any investigation, including any investigation involving Gen. Flynn", the White House said in a written statement. Then-Director of the Federal Bureau of Investigation James Comey testifies in front of the Senate Judiciary Committee during an oversight hearing on the FBI on Capitol Hill May 3, 2017 in Washington, DC.
Some Trump critics say the conversation with Comey was tantamount to obstruction of the FBI's investigation.
This is the latest effort in a newly invigorated push from congressional Republicans to investigate the scandal-plagued White House.
The White House Counsel's office represents the presidency, but aides are making the case to Trump that he needs an outside legal team for this probe.
USA intelligence agencies said earlier this year that Russian Federation interfered in the US election. But Trump pulled him into an embrace and Comey didn't reciprocate. This is the latest in a string of allegations that the Trump administration is in bed with Russian Federation - which the president vehemently denies.
The White House is in a "downward spiral" and needs to do something to get "under control", Republican Senator Bob Corker has said.
Mike Flynn resigned as national security advisor to Trump when it was discovered that he had lied to Vice President Mike Pence about a meeting he had with a Russian ambassador.