The Republican had insisted he would not resign, even if indicted over his dealings with Abramoff. In his first primary test in a decade, Ney won 68 percent of the vote May 2 against a little-known opponent.
But in a statement released by his campaign Monday, Ney, 52, said he had decided to withdraw from his race for a seventh term.
"Ultimately this decision came down to my family. I must think of them first, and I can no longer put them through this ordeal," said Ney, who has denied wrongdoing.
He plans to serve the remainder of his term, his statement said.
Ney spokeswoman Katie Harbath said the congressman was not available for comment.
Earlier Monday, Ohio state Sen. Joy Padgett told The Associated Press that Ney called her Saturday and asked the fellow Republican to run in his place, saying defending himself has been a strain on his family.
"It's a very sad time," Padgett said of Ney's decision, first reported by the Pittsburgh Tribune-Review on its Web site.
Ney told her "just that there's only so much he can take. He said, 'I have to do this,"' Padgett said.
Padgett said she would run for Ney's seat in the 18th district, a conservative region of farms, mines Appalachian hills and Rust Belt cities in central Ohio.
Padgett faces a primary election under Ohio law that requires a primary if a candidate withdraws or dies more than 80 days before a general election. James Lee, a spokesman for Ohio Secretary of State Ken Blackwell, said his office was consulting its lawyers to determine how to proceed. No Republican has come forward to challenge Padgett.
Ney faced a tough challenge in November from Democrat Zack Space, a law director who had made the Justice Department's investigation into Ney a focus of his campaign. Space's campaign did not return a message Monday morning.
Though Ney has not been charged with any crimes, court papers released during Abramoff's plea deal detailed lavish gifts and contributions that Abramoff says he gave an unnamed House member in return for officials acts. Officials have confirmed the congressman is Ney.
Abramoff said the congressman took favors including a 2002 golf trip to Scotland, free dinners and events and campaign donations in exchange for his support of Abramoff's American Indian tribe clients in Texas and the lobbyist's purchase of a fleet of Florida casino boats.
Ney also supported legislation to help a California Indian tribe with taxes and a post office and, as chairman of the Administration Committee, approved a lucrative deal for an Abramoff client to improve cell phone reception in House buildings, the court papers alleged.
Ney and some of his aides, including his chief of staff, William Heaton, have been subpoenaed.
Neil Volz, who was Ney's chief of staff before Heaton, pleaded guilty in Washington in May, admitting he participated in a conspiracy to corrupt Ney, his staff and other members of Congress. The Democratic National Committee said Volz's plea agreement put a "Republican culture of corruption one step closer" to Ney, whom it called "Exhibit A."
For the first three months of 2006, Ney's campaign spent more than it raised, a deficit he blamed on mounting legal costs. In the past three months, it was unusually intense campaigning in his expansive rural district that caused the incumbent to spend $52,675 more than donors gave him, he said.
"I'm embattled and attacked; I understand that," Ney told The AP last month after Space raised about $190,000 more than Ney for the quarter.
Ney told the Tribune-Review that his family had not asked him to drop out, but he wanted to spare them anyway.
"I'm doing this for one reason: my family. My wife and two children have been through enough," he said.
Ney also was frustrated that the scandal was overshadowing his work, the newspaper reported.
Padgett, who said she has known Ney for at least 20 years, was flattered that he and House Majority Leader John Boehner, asked her to run. She said she wished the circumstances were different, "but you have to take life as it's given."