"After a thorough review, it is clear that no candidate has been able to win more than 50 percent and the election goes to a second round," Ahmad Yusuf Nuristani, head of the Independent Election Commission (IEC), said.
Abdullah secured 45 percent of the vote on April 5, with his main rival Ghani on 31.6 percent, according to the final results, which came after weeks of deliberation over fraud allegations.
The results were closely in line with the figures released late last month when counting was completed.
The run-off was originally scheduled for May 28.
"Some sensitive materials that were stocked at IEC headquarters for the second round were destroyed by the Taliban attack on March 29 -- providing those materials again needs time," Nuristani said, explaining the delay.
Abdullah said on Wednesday that his campaign had evidence of fraudulent voting that could have a "significant impact on final results".
Abdullah this week received a major boost with the endorsement of third-placed Zalmai Rassoul, a close ally of Karzai, who has stayed publicly neutral in the election.
The first-round election last month was hailed as a success, with turnout far better than in 2009 and the Taliban failing to launch a major attack despite threats to disrupt the vote.
NJF/NJF