The opposition All People's Congress (APC), whose leader Samura Kamara came in second with 41.16 percent of the vote, believes that the final results announced don't correspond with the total number cast at each polling station.
The party claims that the results were proclaimed even before they were certified locally by the electoral commission officials and the political parties.
President Julius Maada Bio was re-elected for a second term in the first round of voting with 56.17 percent of the ballots, according to results released by the electoral commission Tuesday. 55 percent was needed to avoid a runoff.
International observers noted the "statistical inconsistencies" between the partial results and the final results and denounced "the lack of transparency" in the ballot count, while calling for peaceful dialogue to resolve differences.
The APC also warned against similar discrepancies in the results of Freetown, where the outgoing mayor is a prominent opposition figure.
"The APC party hereby strongly warns the Chief Electoral Commissioner... not to make such pronouncement as it would create chaos in this country," said the statement.
In another statement, the opposition party denounced three incidents involving security forces during the electoral campaign and during a Sunday opposition rally where a woman was killed as security forces attempted to disperse the crowd.
They consider these to be "assassination attempts" on opposition leader Kamara, who was present at the scene on each occasion.
The U.S. ambassador said he was "disturbed" by the "death threats" against observers, which "have no place in a peaceful and democratic society".
The National Security Bureau, a government organisation in charge of homeland security, said the alternative results announced by civil society organisations and the "lack of transparency" denounced in a joint statement by six Western diplomats, could provoke "harmful consequences" and "unjustified tension," despite the fact that the election was generally calm.