0421 GMT November 19, 2019
The move is likely to stir political tension across Afghanistan, and also brings to mind the election Abdullah and his top rival Ghani bitterly contested in 2014 that sparked a constitutional crisis and prompted US intervention, AFP reported.
"We have the most votes in this election," Abdullah said at a news conference, without providing evidence.
"The results will be announced by the IEC (Independent Election Commission), but we have the most votes. The election is not going to go to a second round."
Abdullah's announcement came after one of Ghani's running mates, Amrullah Saleh, on Sunday claimed to have garnered the lion's share of ballots.
"According to our information, 60 to 70 percent of the people have voted for our team," Saleh told Voice of America's Dari- and Pashto-language services.
The claims come even before the IEC has finished tallying turnout from Saturday's election, with hundreds of polling centers still unreported.
Preliminary results are not due until October 19, and if the leading candidate does not secure more than 50 percent of the vote the top two will run off in a second round.
Almost immediately, senior IEC official Habib Rahman Nang slammed Abdullah's announcement as premature.
"No candidate has the right to declare himself the winner," Nang said. "According to the law, it is the IEC that decides who is the winner."
Abdullah, who is seeking the presidency for the third time after losing in 2009 and 2014, said his team would "make the new government".
Without giving details, Abdullah also mentioned reports of "some government officials" meddling in the election process.
His remarks follow the release on social media of several videos purporting to show election workers stuffing ballots in favor of Ghani.
Shortly after Abdullah's comments, EU foreign policy chief Federica Mogherini called on candidates to respect the electoral timeline.
"We expect that the candidates exercise restraint, await the official announcement of preliminary and final results by the (IEC) and submit any evidence-based complaints through the established institutional complaints mechanism," she said in a statement.