Representative Max Miller, the Ohio Republican whose re-election campaign is in jeopardy amid allegations that he abused his ex-wife and toddler daughter, defiantly denied those claims on Sunday and refused to drop out of his race for a third term.

In a livestream that lasted about 20 minutes, Mr. Miller appeared agitated and at times seemed to be laboring to read from a script as he categorically denied the accusations by his ex-wife, Emily Moreno.

The lengthy public statement prompted Ms. Moreno’s father, Senator Bernie Moreno, also an Ohio Republican, to issue a public rebuke of Mr. Miller, saying for the first time after a yearslong legal battle that his son-in-law was not fit to serve in Congress.

The intraparty family conflict has burst into public view days before a Wednesday deadline for replacing Mr. Miller on the ballot in the election for a seat that was once considered a lock for Republicans but now appears competitive.

What are the accusations against Max Miller?

Mr. Miller and Ms. Moreno divorced in 2024 and have battled in court ever since in a custody battle that has included accusations of child abuse, stalking and the filing of restraining orders.

Ms. Moreno has said that Mr. Miller scalded her chest and stomach by throwing hot water from a skillet at her body; held a gun to her head; pushed her against a wall and hit her head; and fractured their daughter’s collarbone and bruised her shoulder.

According to court documents, their daughter at one point told Ms. Moreno, “Daddy kill you.”

Mr. Miller has denied the charges and leveled his own against Ms. Moreno. He has said without evidence that his wife suffers from “significant mental health challenges” and called her a liar, a stalker and a dangerous individual who has made him and their daughter unsafe.

In his appearance on Sunday, Mr. Miller also contended that Ms. Moreno’s claims were not credible because she at times made friendly overtures to him after the episodes of alleged abuse.

“If I had assaulted her,” he said, “would she have offered to cook me dinner six days later?”

He also noted that he retained joint custody of their daughter after years of legal battles, citing that as proof that the courts do not consider him a threat to his family.

“If these accusations were true, I would be in jail,” he said.

How has Senator Bernie Moreno responded?

For months, Mr. Moreno remained silent in the face disturbing details that emerged from court documents that alleged abuse against his daughter and granddaughter. In recent days, he has been heavily criticized online for failing to call for Mr. Miller to resign or end his re-election campaign, in what Democrats said was a sign of allegiance to his party over his own family.

But on Sunday, after Mr. Miller’s defiant livestream, Mr. Moreno broke his silence in an emotional and unequivocal post on social media that hinted at the personal toll the saga has taken on his family.

“If there are any basic standards of character required to hold elected office, Max Miller fails them,” Mr. Moreno wrote. He 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.”

Mr. Moreno, people close to him said, has been paying hundreds of thousands of dollars for the litigation against Mr. Miller, and had been held back from speaking out against him by his daughter.

How have other Republicans responded?

Most Republicans have not criticized Mr. Miller or called for his resignation, many of them noting that the allegations against him have not been proved.

The politics are clear: Republicans are keenly aware that every seat matters as they stare down an electoral map that shows them at risk of losing their House majority. Mr. Miller holds a seat in Ohio’s Seventh Congressional District, once a reliable Republican stronghold that Mr. Trump won by double digits in 2024.

It is not clear whether Mr. Moreno’s unequivocal denunciation of Mr. Miller’s fitness for office will change that in the coming days.

Speaker Mike Johnson has so far sidestepped questions about the situation by noting that any such claims should work their way through an official process run by the House Ethics Committee.

“The key word there is ‘allegation,’” Mr. Johnson has said of Mr. Miller’s case. Mr. Johnson’s spokesman did not respond to a request for comment on Sunday about Mr. Moreno’s denunciation of Mr. Miller.

President Trump elevated Mr. Miller’s political career after growing fond of him when he was a loyal staff member during the first Trump administration. Mr. Trump briefly addressed the matter on Sunday evening at Joint Base Andrews but remained noncommittal. He had previously endorsed Mr. Miller.

“I’m going to look at it,” he said. “I mean, so far, it’s 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.”

What happens now?

Republicans have a deadline on Wednesday for replacing Mr. Miller on the ballot. Mr. Miller has made it clear he has no intention of ending his re-election bid himself.

But internal Democratic and Republican polls show him just one percentage point ahead of the Democratic nominee — and that was before he was denounced by his former father-in-law and before Democrats have spent any money elevating the allegations against him.

The coming days will pose a test of whether there will be enough pressure from the G.O.P. — or from the president and his inner circle — to force Mr. Miller out of the race, or whether they will stand by him.