Over the weekend, 5,000 votes were added to the tally, most of them favoring Abrams, which the campaign has cited in urging that county and state officials not rush the process but work to make sure all ballots are collected and counted.

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The campaign said Abrams would need more than 21,700 additional votes to force a runoff or more than 19,300 to force a recount. The secretary of state’s office reports 21,190 provisional ballots. Abrams’s campaign aides estimate there are at least 26,000 provisional ballots, based on information they gathered from county officials. It is unclear how many of those ballots have been counted or remain outstanding.

“The bottom line is this race is not over. It is still too close to call, and we do not have confidence in the secretary of state’s office,” Lauren Groh-Wargo, Abrams’s campaign manager, said during a conference call with reporters Sunday.

Kemp campaign spokesman Ryan Mahoney said Sunday, “Stacey Abrams and her radical backers have moved from desperation to delusion. Yesterday, military, overseas and provisional ballots were reported throughout Georgia. The counts are in line with publicly available tracking reports. This is not breaking news and does not change the math. Stacey Abrams lost and her concession is long overdue."

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Dara Lindenbaum, the Abrams campaign’s general counsel, said the lawsuit filed Sunday seeks to stop Gwinnett and DeKalb counties, two large Democratic-leaning jurisdictions, from rejecting absentee ballots in which voters have made minor mistakes, including writing the date they completed the ballot instead of their date of birth in the oath section of their ballots. The campaign argues that the counties should try to get in touch with voters and fix the problems rather than just throw out the ballots. The campaign also is asking that officials count the provisional ballots of voters who have moved but whose voter registration records still show their old addresses.