Ruemmler resigned over links to late sex offender after documents released by the US Justice Department showed she accepted gifts from Epstein and advised him on handling media inquiries about his crimes.
"Ruemmler welcomes the opportunity to appear before the committee," the spokeswoman Jennifer Connelly, said in a statement.
"She has done nothing wrong and had no knowledge of any ongoing criminal activity on his part."
Ruemmler was a criminal defence lawyer at the time of her interactions with Epstein and shared a client with him, Connelly added.
Lutnick has also agreed to be probed about his ties to Epstein.
"Secretary Lutnick has proactively agreed to appear voluntarily before the House Committee on Oversight and Government Reform. I commend his demonstrated commitment to transparency and appreciate his willingness to engage with the committee," Representative James Comer, the panel's chair said on X on Tuesday.
The Justice Department in January released millions of new files related to Epstein, including emails that showed Lutnick visited Epstein's private Caribbean island for lunch years after he claimed to have cut off ties.
Lutnick, appointed to his post by President Donald Trump last year, now faces calls from both Democrats and Republicans to resign.
"I look forward to appearing before the committee. I have done nothing wrong and I want to set the record straight," Axios quoted Lutnick as saying.
Last month, Lutnick told lawmakers he "barely had anything to do with" Epstein.
Lutnick said the two men had exchanged only about 10 emails and met three times over 14 years. Lutnick said a lunch with Epstein took place only because he was on a boat near the island and his family was present for the lunch.
Lutnick is one of a host of powerful men in politics, business and entertainment, including Trump himself, who are under fire for their ties with Epstein.
Lutnick also is in the hot seat over apparent contradictions between the newly released documents and his prior remarks about Epstein, who lived next door to him in New York when Lutnick was CEO of Cantor Fitzgerald.
Earlier on Tuesday, a judge granted preliminary approval to an agreement for Epstein's estate to pay a multi-million dollar settlement to resolve a class action lawsuit that accused two of the disgraced financier's advisers of aiding and abetting his sex trafficking of young women and teenage girls.
Boies Schiller Flexner, a law firm representing Epstein victims, announced the settlement - worth as much as $US35 million ($A50 million) - on February 19.
