The special review process will examine hundreds of thousands of ballots that had been left uncounted by computers due to inconsistencies with the tally sheets that were identified by election officials.
The hand count could easily change the election's preliminary result, which gave Conservative Nasry Asfura of the National Party a razor-thin margin of 43,000 votes - out of more than three million cast - over centre-right Liberal Party candidate Salvador Nasralla.
It is unlikely, however, to quiet claims of fraud and demands for a new election by the ruling leftist LIBRE party, whose candidate Rixi Moncada is a distant third in the vote count.
The November 30 presidential election has been rocked by a chaotic vote-tallying process, as well as political clashes and US intervention.
President Donald Trump has backed Asfura, the 67-year-old former mayor of Tegucigalpa, and suggested that Washington's support for Honduras would be conditional on Asfura winning the election.
Nasralla, a television host and three-time presidential candidate, told Reuters he believed Trump's comments had damaged his chances. He has also said he believed the election was marred by fraud.
Both Nasralla and LIBRE have demanded a manual recount of all ballots that were cast but the president of the election council rebuffed them, saying there was no legal basis for a full recount without concrete evidence of irregularities.
Asfura has remained largely silent on the election, saying people should wait for the final results.
On Wednesday afternoon, LIBRE leaders called on their supporters to gather at the presidential palace to protest against what they called an "electoral coup" and interference by Trump.
"Today, democracy in Honduras is in serious trouble. They want to manipulate our democracy and make decisions that only the people should make," President Xiomara Castro told thousands of protesters who were dressed in the ruling party's red colours and chanted "vote-by-vote".
Election officials blamed the stalled manual count of inconsistent tally sheets on LIBRE protesters blocking the building where they work.
"Our officials cannot enter to perform their duties," Ana Paola Hall, president of the National Electoral Council, said on Tuesday night.
On Wednesday, the US Department of State demanded on X that Honduras begin the special review of uncounted ballots.
"Any call to disrupt public order or the CNE's (election council's) work will be met with consequences," the US State Department's Bureau of Western Hemisphere Affairs said .
"The voices of 3.4 million Hondurans must be respected and upheld." Honduras' electoral council has until December 30 to declare the winner of the election, who would assume office at the end of January for a four-year term.
Major international election observers, including the European Union and the Organisation of American States, have expressed concern over the chaotic and delayed vote count but have not reported evidence of systemic fraud.
