Afghanistan's Independent Election Commission said initial results based on 10 percent of the vote from 26 out of 34 provinces showed former opposition leader Abdullah Abdullah in the lead with 41.9 percent.
Long queues continue to form outside polling stations around Kabul, as people defied Taliban threats of violence to cast ballots in what promises to be the country's first democratic transfer of power.
As international combat forces prepare to withdraw by the end of this year, the country is so unstable that the very fact the crucial elections are being held is touted as one of the few successes in Mr Karzai's tenure.
Nearly 200,000 Afghan security forces are out protect polling stations and voters from threatened Taliban attacks.
The Democratic presidential candidate may also have shown his cards on his choice of running mate.
The US president also shared a post on Twitter accusing Dr Anthony Fauci of misleading the public over hydroxychloroquine.
Fears over an impending second wave of coronavirus dominates Wednesday’s front pages.