Charles Brumskine, the presidential candidate of the Liberty Party said he would consider taking legal action if the electoral commission did not halt in announcing the results.
Several reports have claimed that George Weah has already been declared victor of the elections.
The National Elections Commission Chairman Jerome Korkoya announced the results of 1,232 polling places out of the 5,390 in the 15 counties.
With 33.71 percent of polling stations counted, Weah has taken the lead with 39.7 percent (205,218 votes), while Boakai claimed 31.2 percent, (161,413 votes), in a contest to replace President Ellen Johnson Sirleaf, the National Elections Commission (NEC) said.
A victor needs 50 per cent plus one of the total votes cast to avoid a run-off election.
During her years in office, Johnson Sirleaf managed to win $4.6 billion in debt relief and increased government revenue by bringing in mining and palm-oil companies and attracting Chinese investment. In 2014, he won a Senate seat. People everywhere tell him they want to see change. "It reminds Liberians of a lot of good things".
Over the 12-year period she has been in office, the 78-year-old of head of state has received numerous accolades and condemnations in nearly equal measure.
Wenger coached the 51-year-old footballer-turned politician between 1988 and 1992 with the Frenchman being the one who discovered Weah.
"I would like to congratulate one of my former players, who became president of Liberia", he said. "His eyes were glinting, and he spoke with much excitement and a genuine congratulatory feel".
2,183,683 people registered to vote and the NEC says it recorded a high turnout.
Presenting their preliminary finding on the election process, the head of the ECOWAS observer mission and former Ghanaian president, John Mahama lauded the efforts of the Liberian security services in quelling the pockets of violence which arose during voting on Tuesday.