Jimmy Morales has about 25% of the vote so far, with a centre-right businessman, Manuel Baldizon, on 21%.
If no candidate wins more than half the votes, a second round will be held.
Voting took place on Sunday, days after the resignation and arrest of President Otto Perez Molina over corruption allegations.
A new congress is also being elected.Many Guatemalans had called for the polls to be postponed in the wake of the allegations.
If, as expected, no candidate wins 50% of the vote, the second round of voting will take place on 25 October.
“Guatemala wants change and to not be governed by people with dark pasts,” said Mr Morales after voting near Guatemala City.
“Guatemala wants to live in peace. Guatemala wants elections,” Mr Baldizon told journalists after casting his vote.
There had been calls for Guatemalans to wear black clothes of mourning as they cast their vote, amid scepticism that the poll could achieve political change.
“I cast a blank vote in protest as the candidates are all bad, they’re all the same as those who robbed from us,” 34-year-old Josefa Hernandez told Reuters news agency in a suburb of Guatemala City.
“If nobody votes for them, maybe they’ll realise we’re fed up,” she added.
But voters queued from the early hours to cast their ballots.Electoral authorities said 50% of voters had cast their ballots five hours after polls opened.
Some 7.5 million people were eligible to vote in the polls.Prosecutors accuse Mr Perez Molina of masterminding a scheme in which businessmen paid bribes to evade customs charges. He denies involvement.