She predicted she would receive criticism for the tenor of her speech, rather than exhibiting the usual graciousness of a defeated candidate.
Following her announcement, Abrams' campaign sent out a news release that reiterated her comments.
Voters in Georgia reported long lines at polling places as aging technology was swamped by the volume of people seeking to cast ballots. Abrams' campaign had contended there were potentially enough uncounted votes to force a runoff.
Abrams capitalized on the state's shifting demographics and assembled a broad coalition that was eager to deliver a rebuke to President Donald Trump.
Top Abrams advisers outlined her prospective case to The Associated Press, stressing that the Democratic candidate hasn't finalized a decision about whether to proceed once state officials certify Kemp as the victor. Kemp stepped down as secretary of state after declaring himself the governor-elect, but ballots are still being counted, Abrams has not conceded, and media outlets have deemed the contest still too close to call.
Victory for her pioneering campaign would have instantly transformed Georgia into a 2020 presidential swing state and signaled the beginnings of a potential political realignment in region, which has been growing more diverse and educated as its economy expanded. No one answered the phone at her Senate office.
"Under Brian Kemp's watch as the nation's foremost architect of voter suppression, countless Georgians have had substantial roadblocks placed in their path as they sought to exercise their fundamental right to vote".
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The judge requires all counties statewide to accept absentee ballots with minor discrepancies. The state is scheduled to certify results on Tuesday.
He declined to extend the period during which evidence could be submitted to prove the eligibility of voters who cast provisional ballots.
Ms Totenberg's order left untouched the county certification deadline.
A Yale-educated tax lawyer raised by civil rights activists in coastal Mississippi, Abrams ran largely as an unapologetic liberal, promising to expand Medicaid under the Affordable Care Act as a way to address the state's acute rural health care problem.
She did, however, announce plans for a "major federal lawsuit against the state of Georgia for the gross mismanagement of this election and to protect future elections from unconstitutional actions".
Kemp is Georgia's former secretary of state.
When he appeared at the state Capitol last week, he asserted that he had won "a clear and convincing victory" and pledged to "put hardworking Georgians ahead of politics". That could happen as early as Friday evening.
Nearly three dozen lawyers are taking affidavits from people claiming to have been prevented from voting and preparing a court petition.