'We call on all parties to refrain from speculation until the national results are announced,' he said.
A candidate must win 50 percent of the vote to avoid a run-off, which would take place in October.
Afghanistan is conducting its first independently run election in decades, but it has already been plagued with complaints and allegations of corruption. The country has set up a commission to review and potentially investigate complains.
Abdullah held a press conference Tuesday to declare that fraud was 'widespread' and accuse Karzai of playing a role in rigging the vote.