Mr. Miller, who has faced pressure from fellow Republicans to end his campaign and avoid endangering a solidly red seat in Ohio, will stay in the race, his spokeswoman said.
Representative Max Miller of Ohio has denied the accusations against him, which include holding a gun to his ex-wife’s head, throwing scalding water at her and fracturing the collarbone of their daughter.
Republican attacks have focused on terrorism and illegal immigration, while Democrats have sought to capitalize on the unpopularity of President Trump’s cuts to Medicaid.
At a unity rally on Friday night in Detroit, Dr. Abdul El-Sayed, the new Democratic nominee for Senate in Michigan, was joined by other prominent Democrats in the state.