The written request by Rep. Jason Chaffetz, R-Utah, and obtained by The Associated Press, is based on recent revelations from the FBI, which decided not to press for criminal charges after its own yearlong investigation.
Clinton and her longtime aide and lawyer, Cheryl Mills, told FBI investigators during questioning that they had no knowledge of the technology company's deletions.
The FBI's recently released summaries of its investigation did not offer any evidence contradicting their statements.
In a separate letter also obtained by the AP, Chaffetz the House Oversight and Government Reform Committee chairman warned the Denver-based tech firm, Platte River Networks, that one of its engineers who deleted Clinton's electronic files last year could face federal charges of obstructing evidence for erasing the material.
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That's because the congressional inquiry into the 2012 attacks in Benghazi, Libya, in which four Americans were killed, had issued a formal order to preserve such records.
But the sparse evidence laid out in Chaffetz' letters highlighting a March 2015 phone discussion between the tech firm and Clinton lawyers that FBI agents were unable to detail also shows the uphill climb the committee faces in turning up any significant new information beyond what the FBI already learned in its inquiry.
The new requests follow a similar attempt last month by Republican-led committees in the House and Senate to prod new information from the Denver firm as the presidential race between Clinton and Republican candidate Donald Trump enters its critical final months.