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 Mr 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 6% 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 Mr Nasralla.
64-year-old former TV presenter and sports journalist
Heads the Opposition Alliance Against the Dictatorship, a coalition of parties from the left and the right
His parents are of Lebanese descent
Ran for the presidency in 2013 but lost to Juan Orlando Hernández
Has campaigned on a promise to battle corruption
Juan Orlando Hernández
Heads the right-wing National Alliance
Is the 15th of 17 children, two of his siblings are also in politics
Is the first Honduran president to run for a second term after the supreme court lifted a ban on re-election
Says that if elected, he will continue fighting Honduras's influential criminal gangs