"We have got the most votes in the election," Abdullah, President Ashraf Ghani's main rival, told reporters in the Afghan capital.
"In the current situation, the elections will not go to a second round and we will form a new government," he said, according to Efe news.
However, the Independent Election Commission said no candidate had the right to announce election results or claim victory.
"It is the responsibility of the Election Commission to ( ) announce the primary result," said Habib Rahman Nang, a senior IEC officer, denouncing Abdullah's claim as premature.
He said there was still a long process before the poll panel would announce the final result, after assessing all election-related fraud and rigging complaints.
The voting to elect new the Afghan President was held on Saturday amid violence and Taliban threats.
The preliminary results of the polls will not be known till October 19, with the final count expected to be announced on November 7.
If there is no clear winner or no candidate bags over 50 per cent of the ballots cast, a second round of voting will be held to choose between the two contenders who got the most votes.
Abdullah admitted that the turnout was not "as high as was expected", attributing it to security threats and warnings by militants.
He said that despite the threats, a "significant number" of people had turned out to vote.
This was the fourth time Afghans went to the polls to elect a President since 2001, when the US-led coalition ousted a Taliban regime.
( With inputs from IANS )