Republican Congressman John Linder defeated Barr for the GOP nomination as the two incumbents were pitted against each other in a newly drawn 7th Congressional District based largely in Linder's old district.
"We had a hard-fought battle. It's apparent that he won," Barr said.
With 83 percent of precincts reporting, Linder, who has proposed replacing the Internal Revenue Service with a national sales tax, had a 67 to 33 percent lead over Barr, who was best known nationally for leading the House impeachment proceedings against former President Bill Clinton.
"Barr waged a very aggressive campaign in Gwinnett County and apparently it backfired," said Emory University political scientist Merle Black.
McKinney, a five-term congresswoman, was defeated by former DeKalb County Judge Denise Majette for the Democratic nomination in the state's 4th Congressional District, which includes Atlanta's eastern suburbs.
Majette had a 60 to 40 percent lead over McKinney with 95 percent of precincts reporting, based on unofficial returns.
Substantial contributions from outside of Georgia funded both candidates' campaigns. Majette received substantial contributions from local and national Jewish groups, while McKinney, whose outspoken views on the Middle East and the war on terror brought her donations from the Arab-American community.
Majette was apparently helped by Republicans who chose a Democratic ballot so that they could vote against McKinney. Georgia does not require voters to register a party affiliation.
The Georgia Secretary of State's office said it was investigating recorded telephone calls made Monday night that told Republicans "it is a violation of state and federal law to attempt to vote in a Democratic primary without proper documentation."
State officials said they were examining whether the misleading calls violated a Georgia law against intimidating voters. They also said the calls appeared to violate campaign laws requiring any recorded message to disclose the name and phone number of the sponsoring organization.