A senior official at the attorney general's office, Danelia Ferrera, said 357 people died in the blaze that began late on Tuesday night (local time) at the prison in Comayagua, about 75km north of the capital Tegucigalpa.
"It's a terrible scene ... Our staff went into the cells and the bodies are charred, most of them are unrecognizable," Ferrera told Reuters, adding that officials would have to use dental records and DNA in many cases to identify those killed.
It was one of the worst prison fires ever in Latin America.
"We heard screaming from the people who caught on fire," one prisoner told reporters, showing the fingers he fractured in his escape from the fire. "We had to push up the roof panels to get out."
Honduras has the highest murder rate in the world, according to the United Nations, and there are frequent riots and clashes between rival street gangs in its cramped prisons.
But it was not yet clear if the prison fire was started during a riot or if it was an accident.
Worried and angry relatives surrounded the prison on Wednesday morning, at one point throwing rocks at police and trying to force their way inside the prison.
Police responded by firing shots into the air and shooting tear gas at protesters, most of whom were women.
President Porfirio Lobo said he suspended the director of the Comayagua prison and the head of the national prison system to ensure a thorough investigation.
He promised to "take urgent measures to deal with this tragedy, which has plunged all Hondurans into mourning".
There was confusion over the death toll, with some reports that more than 100 inmates had escaped and could have been mistakenly counted among the dead and others that the dead and missing totalled 402 people - almost half the prison's inmates.
Lucy Marder, head of forensic services in Comayagua, said police reported that one of the dead was a woman who had stayed overnight at the prison and the rest were inmates, but she said some of the presumed dead could have escaped.
Local media reported that the Comayagua fire department chief also died in the blaze.
Honduras' notoriously violent street gangs, known as 'maras', gained power inside Hispanic neighborhoods in the United States in the 1980s and then spread down into Central America. Their members wear distinctive tattoos and are involved in drugs and weapons trafficking, armed robbery and protection rackets.
The Comayagua prison housed more than 850 inmates -- well above its capacity. A local police chief read out the names of 457 survivors outside the prison, but relatives were not appeased.
"This is desperate, they won't tell us anything and I think my husband is dead," a crying Gregoria Zelaya told Canal 5 TV as she stood by a chain link fence.
Local firemen said they were prevented from entering the prison due to gunshots. But Daniel Orellana, head of the prison system, said there was no riot.
"We have two hypotheses, one is that a prisoner set fire to a mattress and the other one is that there was a short circuit in the electrical system," he said.
Across Honduras, prisons are filled to double their capacity with about 12,500 prisoners in jails meant to hold 6,000. More than 100 prisoners were killed in a fire in the textile manufacturing town of San Pedro Sula several years ago, and survivors said later that guards fired on prisoners trying to escape the blaze.
Honduras had more than 80 homicides per 100,000 people in 2009, a rate 16 times that of the United States, according to a United Nations report last year.
The country is a major drug trafficking transit point for South American cocaine moving north to consumers in the United States, and authorities say there is increasing presence of violent Mexican drug cartels in the country.
A political crisis ripped through Honduras in mid-2009 when a widely-condemned coup toppled the democratically elected president but the country has been trying to heal divisions since Lobo was elected later that year.
