The electoral tribunal has said Hernandez won, scoring 34 per cent compared to the 29 per cent of his rival, with 68 per cent of polling stations tallied.
Castro and her husband, deposed ex-president Manuel Zelaya, allege that the Supreme Electoral Tribunal manipulated 19 per cent of the votes to favour Hernandez.
They gave 48 hours for the situation to be resolved.
"We will defend the will of the people as it was expressed at the polls," Castro wrote in a Twitter posting.
Tensions were running high as the political standoff exploded into violence on the streets of Tegucigalpa yesterday.
Police beat and used tear gas against about 800 people demonstrating in support of Castro.
"Why are the people asked to come out and vote if they are not going to respect the result? There has been a massive fraud here," said student Carlos Garcia.
Students fled from police, running to their nearby campus, and at the entrance gates authorities lobbed more tear gas at them. The university called off classes for two days as post-electoral tensions deepened.
Hernandez is a law-and-order conservative who has promised a militarised program to improve public safety in the world's deadliest nation, also among the poorest in Latin America.
Gangs run whole neighbourhoods, extorting businesses as large as factories and as small as tortilla stands, while drug cartels use Honduras as a transfer point for shipping illegal drugs, especially cocaine, from South America to the United States.
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