0452 GMT July 18, 2018
The Electoral Tribunal had already agreed to an earlier opposition demand for a partial recount, BBC reported.
The opposition candidate, Salvador Nasralla, had been set for victory when the tally unaccountably stopped.
President Hernandez then went into the lead, sparking days of street protests.
The Honduran government is facing mounting pressure to accept further recounts after a police rebellion and criticism from international observer missions of voting irregularities.
Hundreds of members of the Honduran riot police force known as Cobras had refused to carry out orders to enforce a night-time curfew on Monday.
About 200 Cobras gathered at the police headquarters and announced they were no longer willing to confront protesters, arguing that it amounted to "taking sides" in the political battle between Nasralla and President Hernández.
"We are rebelling. We call on all the police nationally to act with their conscience," one masked officer told Reuters news agency.
Reports said police in other cities had also joined their Cobra colleagues in the strike.
Earlier, election monitors from the regional body, the Organization of American States (OAS), said that "irregularities, errors and systematic problems" with the presidential election on 26 November meant they could not be certain of the result.
The head of the observer mission, Jorge Quiroga, had also urged the Honduran authorities to carry out a wider rechecking of ballots.
Electoral authorities counted about six percent of the votes again on Monday and agreed a day later to look at ballots from 5,173 polling stations — nearly a third of the total.
OAS observers said that the problem had been "the ballots had not been transmitted on the night of the election, and a recount of tallies shows inconsistencies."
But after the Supreme Electoral Tribunal agreed to the wider recount, the leader of the opposition alliance, former president Manuel Zelaya, demanded a full run through the votes.
President Hernández has called for "brotherhood, for sanity, for national unity".
The electoral tribunal website suggested that with 99.98% of the votes counted, President Hernández had a lead of 1.6 percentage points over Nasralla.