At the time of going to press, the results were: Joseph N. Boakai...... (UP) 748,463 (43.70%) and George M. Weah....... (CDC) 747,578 (43.65%), KMTV Liberia reveals.
According to BBC, a run-off will be held if neither candidate gets more than 50%.
Mr Weah, a former football star, won a run-off in the 2017 poll with 61.5% to Mr Boakai's 38.5%.
He had won the first round with 38.4% of the vote, compared with Mr Boakai's 28.8%, suggesting that Mr Boakai is faring better in this election.
By Sunday, Liberia's elections commission had tallied votes from 4,295 of the 5,890 polling stations.
The body has 15 days from the date of the election to announce the final results. If there is no outright winner, a run-off will be held on 7 November.
More than 2.4 million Liberians, many of them first-time voters born after the 1989-2003 civil wars, had registered to elect the president, members of the House of Representatives and half the Senate.
Local and regional election observers reported peaceful polls and a high turnout across the country, but cited problems such as voting delays at some polling stations.
Despite the slow announcement of results, the West African regional bloc Ecowas, of which Liberia is a member, has asked Liberians to "continue to exercise maximum restraint as they wait for official provisional results".
Ecowas also said that it was aware of "attempts by some Liberian stakeholders to declare premature victories or put undue pressure on the National Elections Commission".
It warned that such groups would be held "accountable for any actions that may lead to violence and instability".
Liberia is recovering from the brutal civil wars that ended two decades ago, after killing an estimated 250,000 people.
Analysts say this might be the last attempt at the presidency for Mr Boakai.
The 78 year old, a former vice-president, has waged his campaign under the slogan "Rescue", arguing that the West African state went downhill during Mr Weah's first six years in office.
Mr Weah, 57, has dismissed Mr Boakai's allegations, saying that he made significant strides in his first term, including introducing free tuition for university students.
The secretary-general of Mr Weah's ruling Coalition for Democratic Change (CDC) party, Jefferson Koijee, last week ruled out the possibility of Mr Weah losing, but said that the president would accept the result because "the peace of this country is above his own".
