Jimmy Morales, who has campaigned against corruption, 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 September 6, days after the resignation and arrest of President Otto Perez Molina over corruption allegations.
A new congress is also being elected.
Many voters had called for the polls to be postponed in the wake of the allegations.
If no candidate wins 50% of the vote, the second round of voting will take place on October 25.
“Guatemala wants change and to not be governed by people with dark pasts,” said Jimmy Morales after voting near Guatemala City.
“Guatemala wants to live in peace. Guatemala wants elections,” Manuel 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 skepticism that the poll could achieve political change.
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 Otto Perez Molina of masterminding a scheme in which businessmen paid bribes to evade customs charges. The former president denies involvement.
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