The pistols and revolvers were thrown into a furnace in the capital Kingston, watched by police and officials from the government and the UN.
Jamaica has one of the highest rates of gun crime in the world.
Correspondents say criminal gangs are often as well armed as the security forces.
Officials said about half a ton of ammunition would also be destroyed in the operation.
Many of the guns had been seized in police operations. However, old firearms from police, military and prison personnel were also destroyed to ensure they did not end up in the hands of criminals.
National Security Minister Peter Bunting said the programme was just the first step towards reducing the stockpiles of illegal guns on the Caribbean island.
“The removal will help to reduce the risks of these weapons being possibly diverted back into the illicit trade,” he said.
UN co-ordinator William Godnick said destroying the guns was “the beginning of a long process in which we hope to destroy a much larger quantity”.
The BBC’s Nick Davis in Kingston says that although gun crime has long been a problem in Jamaica, the murder rate has been falling. However, the authorities want to do more.
Between 70-80% of fatal shootings have been linked to criminal gangs whose firepower equals that of the police, our correspondent adds.
On Wednesday the ammunition will be destroyed and in the next few days another 2,000 firearms are also due to be melted down.