Political parties have expressed concern over polling-day hitches on Tuesday that have caused significant delays to the results, with one party calling for a halt to the ballot counting.
Weah and Boakai are expected to top the first round of voting, according to analysts, though former Coca-Cola executive Alexander Cummings is considered to have eaten into their support with an innovative campaign strategy.
The only county with more than 30 percent of votes counted -- Bong county -- showed Boakai and Weah neck-and-neck with a slight advantage on Weah's side.
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Weah was also leading in Montserrado county, his stronghold, which although just 14.8 percent of ballots have been counted dwarfs Liberia's other counties in representing 778,000 voters.
If no candidate wins over 50 percent of the presidential vote nationwide, a run-off between the top two contenders will be held on November 7 -- an outcome deemed a near certainty.
Jerome Korkoya, NEC Chairman, said the commission was "committed to the release of timely results but this cannot be done at the expense of accuracy," after foreign observers began to apply pressure over the long wait.
"This commission has not declared any winner," Korkoya added, saying the results remained too partial to declare a runoff.
Korkoya also hit out at false reports including a tweet by Arsenal manager Arsene Wenger that Weah had already been declared the winner.
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"Reports going around that somebody or some people have already been elected, we are not aware of that," the NEC chairman said.
The chairman of the Liberty Party, whose candidate is not expected to make the run-off round, on Thursday urged the "NEC to immediately halt further announcements of election results."
"If NEC does not cooperate with our request, we will take the appropriate legal action," the party's chairman, Ben Sanvee, said.
Turnout for Liberia's first democratic transfer of power in seven decades was exceptionally high, the NEC has suggested.
Given the delays, the European Union observer mission had urged the NEC to be as open as possible about the details of the final results.
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"In order for the final result to be credible, the Liberian authorities will have to show the greatest transparency regarding the handling of the result for the polling stations until the validation," the chief observer of the EU's Election Observation Mission, Maria Arena, told journalists in Monrovia.
She also called on the authorities to ensure that "potential complaints are handled with the utmost impartiality" in a tense environment.
The Carter Center, an NGO founded by former US president Jimmy Carter, said "prompt release of results" would help in "building confidence among the electorate and preventing confusion and tension."
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