As chairman of the House's top investigative committee, Chaffetz is looking into whether Trump tried to pressure the former FBI director to stop an investigation of former national security adviser Michael Flynn.
"I have my subpoena pen ready", he tweeted.
The Senate intelligence and judiciary committees both sent requests for Comey's documents, detailing his conversations with Trump.
The requests came a day after the New York Times published a report, subsequently corroborated by other outlets, detailing the existence of a memo written by Comey describing a meeting in which Trump asked him to drop an investigation into the Russian Federation ties of his sacked national security adviser Michael Flynn.
The head of the Republican Study Committee, Rep. Mark Walker, said that if the report is true, then it's concerning to him.
The White House responded to the New York Times report by saying that the story was "not a truthful or accurate portrayal of the conversation" between Trump and Comey.
Leaders of the congressional investigations into Russian meddling into the USA election previous year are also calling on Comey to testify.
From the White House Counsel, the senators asked for "records of interactions with former Director Comey, including any audio recordings". "I think it would be good for him if he did".
Grassley said Wednesday it was a "foregone conclusion" the judiciary committee would hold a hearing on the Comey memos and the FBI Russia investigation.
"OK, well, he's got to come in and tell us why", Graham said.
"Today, The New York Times reported former Federal Bureau of Investigation Director James Comey memorialized the content of the phone calls and meetings with the President in a series of internal memoranda", Chaffetz wrote in the letter.
"At best, President Trump has committed a grave abuse of executive power".
Flynn, a former military intelligence chief, had been forced out of his White House job the day before Trump's meeting with Comey over concerns about his contacts with Russian officials.