Representative Max Miller, the Republican from Ohio accused of physically abusing his ex-wife and young daughter, has defied calls from his own party to drop out and plans to stay in the race to keep his seat in Congress, according to his spokeswoman.

Mr. Miller would have had to withdraw by Saturday evening, at the latest, to allow local party chairs enough time to name a replacement on the ballot by Monday at 4 p.m., according to Ohio state law.

His decision, confirmed by Abigail Angelos, a campaign spokeswoman, sets up a competitive general-election campaign. Mr. Miller’s district was considered solidly Republican before his divorce from the daughter of Senator Bernie Moreno of Ohio and the public allegations of physical abuse that followed.

Mr. Miller has denied the accusations, which include holding a gun to his ex-wife’s head, throwing scalding water at her and fracturing the collarbone of their daughter.

Over the past week, pressure mounted from within his party for him to step aside. President Trump called Mr. Miller, a former aide to the president, to encourage him to look carefully at his odds. Senator Jon Husted of Ohio, a Republican also up for re-election, described him as unfit for office and urged him to resign from Congress. White House staff members and Republican officials in Ohio have privately conveyed concerns that his personal problems could cost the party a seat as it tries to keep control of the House.

But Mr. Miller has been resolute all week that he planned to do what Mr. Trump had done when faced with his own personal scandals: stay in and fight. He has defended himself in a media tour that left some in his own party worried about his mental state and alarmed at the prospect of his continued candidacy.

In November, he will face Brian Poindexter, a union-card-carrying ironworker who Democrats believe can defeat Mr. Miller with an appeal to the working-class voters in Ohio’s Seventh District.

The Ohio Republican Party and local party chairs stayed publicly quiet this week, for the most part, declining to answer questions about whether they supported Mr. Miller’s candidacy.

If Mr. Miller had withdrawn, they would have had to call a meeting by the end of Saturday to replace him, under state law.

Matt Miller, the chairman of Ashland County and the mayor of Ashland, who is not related to the congressman, said on Saturday that no such meeting had been scheduled.