The Republican-led Committee on Education and the Workforce shared its plans to widen its scrutiny of Dr Gay's handling of antisemitism on Harvard's campus.
Chairwoman Virginia Foxx said the inquiry would see if students and staff are held to the same academic standard.
The BBC contacted Harvard's governing body for comment.
Ms Foxx, a Republican member of the House of Representatives, said in a letter to the leader of Harvard's board on Wednesday that the prestigious institution could be violating the public's trust.
"Our concern is that standards are not being applied consistently, resulting in different rules for different members of the academic community," she said.
Harvard is a private institution that receives hundreds of millions of dollars of public funding each year. It has $50bn (£40bn) in assets.
The university's governing board said last week that it had checked Dr Gay's academic history and had found "instances of inadequate citation".
But it added that she did not violate "standards for research misconduct".
The letter demands that Harvard submit any documents and communications related to the plagiarism inquiry into Dr Gay, as well a list of any academic disciplinary actions taken against Harvard faculty or students since 2019.
It asks that the board respond to the committee by 29 December.
"If a university is willing to look the other way and not hold faculty accountable for engaging in academically dishonest behavior, it cheapens its mission and the value of its education," Ms Foxx said.
Harvard's board has said it became aware of plagiarism allegations against Dr Gay in October, but has unearthed no violations of Harvard policies.
US students grapple with free speech and antisemitism
Recent reports published by US outlets CNN and the Washington Free Beacon claim further instances of plagiarism. This includes her 1997 dissertation in which she allegedly copied a full paragraph nearly verbatim from a paper published one year earlier.
The Free Beacon, a conservative publication, said it has discovered at least 29 cases of plagiarism.
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Dr Gay has faced calls to resign from her post for her testimony during a congressional hearing before the same committee now investigating Harvard and other prominent US universities.
She and other university leaders were accused of insensitivity and hypocrisy when discussing efforts to stem antisemitism on their campuses amid the Israel-Gaza war.
During tense questioning, Dr Gay said calls for the killing of Jews were abhorrent. She added, however, that it would depend on the context whether such comments would constitute a violation of Harvard's code of conduct regarding bullying and harassment.
The university later announced it had chosen not to discipline Dr Gay for her testimony, and she also apologised in an interview with the school's student newspaper.
By Max Matza