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 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.