Uncertainty is growing around the outcome of the election, already marred by record-low turnout and continued disputes between Abdullah and his long-time rival, President Ashraf Ghani.
Initial results were supposed to have been released on October 19 but the announcement has been delayed twice, with election officials citing various technical problems.
A new date for the announcement has been set for Thursday, but officials have hinted it will be pushed back yet again as bickering continues over the counting process.
Abdullah on Sunday said recounting should be stopped until the Independent Election Commission addressed his concerns that some 300,000 of the approximately 1.8 million votes were not valid.
In a statement, the Election Support Group - comprised of key international donors including the United States, the European Union, NATO and the UN - said candidates should respect election law and "refrain from any actions or statements that undermine the process".
"The ESG urges all candidates to cooperate with the recount and audit process and follow the formal ... complaints process to raise their concerns about the alleged irregularities," the statement said.
The ongoing dispute over the vote raises the possibility Afghanistan is headed for a repeat of the crisis that followed the last presidential election in 2014. Then, Ghani and Abdullah fought a close and angry race that sparked widespread allegations of fraud and saw the US step in to broker an awkward power-sharing agreement between the rivals under a unity government.