Representative Max Miller, the Ohio Republican whose tight re-election campaign has been rocked by accusations of domestic violence against his ex-wife and their toddler daughter, said on Sunday that he was “not getting out of this race.”

He made his defiant statement as concerns grew among Republicans that what had been a safe seat for the party could be in danger. The statement also evoked an emotional response from his former father-in-law, Senator Bernie Moreno of Ohio, who said that Mr. Miller is not fit to hold public office. Mr. Moreno, who has been silent until now about the very public battle, said the dispute has put his family through “pure hell.”

In a roughly 20-minute livestream on X that Mr. Miller previewed as a “special announcement,” he categorically denied all the accusations that his ex-wife, Emily Moreno, the daughter of Mr. Moreno, has leveled at him in court. He also claimed she had “significant mental health challenges.”

His announcement came just three days before the deadline for Republicans to replace Mr. Miller on the ballot, locking him in as the G.O.P. nominee for a seat that has become competitive in large part because of the allegations against him. Mr. Miller appears just one percentage point ahead of his Democratic challenger, according to internal polling research by Democrats, in a district that President Trump won by double digits in 2024.

In his livestream on Sunday, Mr. Miller said he had never scalded Ms. Moreno’s chest and stomach by throwing hot water from a skillet at her body, as she has accused him, dismissing the incident as “horseplay in our kitchen” with water that was not boiling.

He also denied her accusation that he held a gun to her head, and he vehemently rejected her charge that he had fractured their daughter’s collarbone and bruised her shoulder.

Mr. Miller, a former staff member for Mr. Trump, blamed his daughter’s injuries on two day care workers.

“If these accusations were true, I would be in jail,” Mr. Miller said, seated in his kitchen and reading haltingly from a script. He contended that the credibility of her assertions was undermined by the fact that he still retains joint custody after years of court battles.

Until Sunday, Mr. Moreno had said almost nothing regarding the matter.

But after Mr. Miller’s livestream, Mr. Moreno posted a long response on social media. He wrote that “if there are any basic standards of character required to hold elected office, Max Miller fails them” and added, “I hold my breath every minute he has custody of my granddaughter.”

He continued: “He should not serve in the House of Representatives. I believe Max Miller needs to seek professional help to end the clear pattern of abuse he has left in his wake. I believe he should not be free to continue endangering others until he does.”

In his livestream, Mr. Miller repeatedly pointed to examples of what he claimed were friendly overtures from Ms. Moreno as proof that she was fabricating the claims of abuse. “If I had assaulted her, would she have offered to cook me dinner six days later?” he asked.

Ms. Moreno is seeking to end their shared parenting agreement. The issue is expected to go to court on Nov. 5. Last week, Ms. Moreno filed a restraining order against Mr. Miller, claiming he had harassed and threatened her lawyers.

Immediately after his livestream, Mr. Miller made public a trove of recordings, text message exchanges and court documents that he said would prove his innocence. A lawyer for Ms. Moreno did not immediately respond to a request for comment.

As Democrats have called for a House Ethics Committee investigation into the allegations against Mr. Miller, Republicans have stayed silent publicly across the board. Speaker Mike Johnson has said only that there is an ethics process for handling with such accusations.

Representative Jim Jordan, Republican of Ohio, defended Mr. Miller in a recent interview. “This is a family matter. I know Max is a good man,” he told CNN. “I hope he wins re-election.”

Behind the scenes, however, Republicans in Mr. Trump’s orbit have said they are alarmed by Mr. Miller’s decision to go on the offense against Ms. Moreno and are concerned about his re-election campaign.

Mr. Miller, however, expressed deep confidence on Sunday that he would be back in Congress next year.

“This election to me is about my family and about our daughter and keeping our values here and holding the media and other individuals accountable,” he said.

Ms. Moreno is not the first woman to level domestic abuse allegations against Mr. Miller. In her memoir, Stephanie Grisham, the former White House press secretary, wrote that she dated someone in the administration who was physically abusive. She later acknowledged that she had been referring to Mr. Miller.