People wait in line to vote in the Georgia's primary election at Park Tavern on Tuesday, June 9, 2020, in Atlanta.
Ossoff was far ahead of two other candidates in his bid to challenge Republican U.S. Sen. David Perdue in November.
In Georgia, candidates must win more than 50% of the vote to avoid a runoff.
Perdue, a close Trump ally seeking a second term in November as Republicans look to hold the White House and Senate majority, drew no GOP primary opposition.
Ossoffs campaign manager, Ellen Foster, blasted Republican Georgia Secretary of State Brad Raffensperger for the long lines and confusion at numerous polling sites Tuesday.