Provisional results published Tuesday by the NEC show that 94% of the ballots have been counted and Boakai has 43.70% while Weah has 43.65%.
NEC's results showed that the rivals were well ahead of the 18 other presidential candidates in the first round of voting of the West African nation’s Oct. 10 elections.
Ballot counting is now complete in nearly 93 percent of polling stations, NEC said on its website.
The figures indicate that neither Weah nor Boakai are set to secure enough votes for an absolute majority and be elected in the first round.
A run-off is planned for two weeks after the announcement of official results but could be delayed by possible appeals.
West Africa's regional ECOWAS bloc and the African Union have congratulated Liberia's government and the election commission for the organization of a peaceful vote, marked by a high participation rate.
Despite the congratulations by the regional bodies, Boakai and other members of the opposition Unity Party, UP, allege that the incumbent president is tampering the vote — allegations vehemently denied by the ruling Coalition for Democratic Change, CDC.
In an interview with VOA, Eugene Nagbe, the campaign manager for the CDC said the elections were democratic.
The opposition's allegations of vote tampering are "because they are seeing from the results that they are losing and therefore they have no recourse but try and accuse the president when he is away from the tallying process," Nagbe added.
Liberia's Oct.10 elections were the first to be held since the United Nations ended its peacekeeping mission in Liberia in 2018.
The mission was created after more than 250,000 people died in two civil wars between 1989 and 2003.
Information for this article was sourced from Agence France Presse. VOA’s James Butty contributed to this article.