Leftist TV host-turned-politician Nasralla said Hernandez was colluding with the army and the electoral authorities to forge new results sheets and give himself the edge in Sunday's presidential election.
"He's fabricating (the results)," Nasralla told AFP in an interview.
"He controls the media. He's going to have the results sheets he wants validated and change the will of the people."
The election in this poor, gang-plagued country has turned into a drawn-out showdown between Nasralla, 64, and Hernandez, 49, who is going for four more years in office despite a constitutional limit of just one term.
Both candidates have declared victory, but the results are far from clear.
In the early hours of Monday, Nasralla led by five percentage points with 57 percent of ballots counted.
Then the Supreme Electoral Tribunal interrupted its live broadcast of the results and announced the rest of the ballots would be brought to the capital, Tegucigalpa, to be counted.
On Tuesday, the election authority posted new results on its website: 44.4 percent for Nasralla to 40.5 percent for Hernandez -- about one percentage point narrower than the opposition candidate's previous lead -- with just over 61 percent of the ballots counted.
Nasralla accused the conservative president of plotting to rig the vote, saying his "survival instinct" was hijacking democracy.
"He knows if he's not the president any more he'll be extradited" to face corruption charges, he told AFP.
"He's trying to sow chaos so he can declare a state of emergency and take control with the help of his people and the army."
President urges patience
Hernandez for his part asked Hondurans to be patient.
Officials have said the final vote tally may not be ready until Thursday.
In his first public appearance since declaring himself winner Sunday night, Hernandez said his supporters are right to take to the streets in celebration, as they have done.
Speaking at a press conference, he again insisted he has won the presidency and his party the largest number of seats in congress.
"The result is more than clear," he said at the presidential residence.
But Hernandez also said people must wait until all the ballots are counted.
"It is important for everyone to be patient, for everyone to be considerate with Honduras," he said.
Hernandez's conservative National Party -- which controls the executive, legislative and judicial branches of government -- contends that a 2015 Supreme Court ruling allows his re-election.
Nasralla and his coalition, the Opposition Alliance Against the Dictatorship, have denounced the incumbent's bid, saying the court does not have the power to overrule the 1982 constitution.
Situated in the heart of Central America's "Northern Triangle," where gangs and poverty are rife, Honduras has one of the highest murder rates in the world -- though it has fallen under Hernandez.
What credit he claims from that progress, however, is counterbalanced by tensions over his re-election bid.
It is a loaded issue in Honduras, where former president Manuel Zelaya was toppled in a coup in 2009 -- notably because he was accused of plotting to change the constitution to stand for a second term.
Nasralla has close ties to Zelaya, who remains a popular figure.
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