The dramatic move comes as Comer asserts Wray is refusing to fully comply with a subpoena to turn over an unclassified FBI-held document or documents that, Republicans say, link Biden to a $5 million "bribery scheme" involving an unnamed foreign national.
If a majority of the Oversight Committee agrees to hold Wray in contempt, the measure would be sent to the full House for a floor vote and a likely referral to the Justice Department.
The FBI said in a statement on Monday that had "demonstrated its commitment to accommodate the committee's request, including by producing the document in a reading room at the US Capitol."
"The escalation to a contempt vote under these circumstances is unwarranted," the bureau said in the statement.
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A spokesperson for the Justice Department declined to comment. A White House spokesman, Ian Sams, said in May that the effort to get the document was part a Republican campaign of "lobbing unfounded, unproven, politically-motivated attacks against the president and his family without offering evidence for their claims."
Justice officials are unlikely to prosecute Wray, but an extended civil court battle between two branches of government could ensue.