Hernandez had 34 percent of the votes to 29 percent for Castro in an eight-candidate field, according to the most recent returns, with about a third of the votes still uncounted.
"It's not the final result, but it's an irreversible trend," tribunal spokeswoman Lourdes Rosales said.
Electoral officials said they hoped to have final results by Thursday, but they didn't explain why it was taking so long to finish the vote count. The tribunal reported results from 54 percent of the votes by late Sunday, but barely advanced the count over the next two days.
About 200 university students blocked a major thoroughfare in the capital Tuesday to protest what they said were fraudulent election results and demand a recount. The students clashed with police officers who threw tear gas at the crowd.
Election observers for both the European Union and Organization of American States issued statements Tuesday describing the election and vote count as transparent.
Dario Euraque, a professor of history and international studies at Trinity College in Hartford, Connecticut, said Hernandez's candidacy resonated with Hondurans because he pushed through legislation giving the military a role in patrolling some of the country's crime-beset cities.
"Military presence is key when you practically have a failed state," Euraque said. "It's a mistake to ask they retire (to their barracks). People don't understand it. They want security and will accept that discourse."
Hernandez will likely face a divided Congress, whose 128 members were also elected Sunday. As a result, the political situation is unlikely to change dramatically in this failing state of 8.5 million people, which is home to the world's highest homicide rate and widespread poverty. Those working for less than the minimum wage of $350 a month have grown from 28 percent of the work force in 2008 to 43 percent today.
Honduras also has been a focal point for U.S. drug enforcement efforts as the transit point for much of the South American cocaine heading to the U.S.
Hernandez, a lawyer and reserve army lieutenant who became president of congress in 2010, said Honduras needs an anti-drug strategy with the U.S. that is more effective.
"For them it's a problem of public health, but for us it's a problem of blood and death," he said during the campaign "We expect that the stage that's about to begin will be more effective than the one in the past."