Hundreds of members of the Honduran riot police force known as Cobras refused to carry out orders to enforce a night-time curfew on Monday.
The electoral authorities say incumbent Juan Orlando Hernández has an unassailable lead but have not yet officially declared him the winner.
Rival candidate Salvador Nasralla has cried foul and his supporters have been on the streets protesting.
At least three people were killed as protests turned violent last week.
'Act with your conscience'
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.
"Our people are sovereign. We cannot confront and repress their rights," another officer said reading a statement.
Some of the striking police joined supporters of Mr Nasralla who were demonstrating in the streets in defiance of the curfew.
They were cheered by the protesters, some of whom held up signs reading "I love the police!".
Reports said police in other cities also joined their Cobra colleagues in the strike.
Earlier, election monitors from the regional body, the Organization of American States, 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, also urged the Honduran authorities to carry out a wider recount of ballots.
Electoral authorities carried out a recount of about 6% of the votes on Monday and have not ruled out a wider recount.
President Hernández called for "brotherhood, for sanity, for national unity".
Unlike in previous public appearances, the president did not claim victory on Monday.
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
- 49-year-old lawyer
- 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