The men, who police said held Chinese passports, stormed the store with BB-guns in an effort to steal real firearms.
But the were thwarted after the owner of the store opened fire on the robbers.
Armed police quickly joined in the firing and three of the raiders were wounded, with one dying later in hospital.
Officers are still hunting for the leader of the network, who they said has entered Thailand several times.
"Their purpose was to steal guns but we don't know what they planned to use the guns for," he said, adding the men were Mongolian.
The besieged store, "Inter Arms", is on a popular street for trendy bars and restaurants in the capital city's historic Chinatown neighbourhood.
Gun ownership is widespread in Thailand and watchdog groups say the kingdom has one of the highest gun murder rates in Asia.
The Thai government does not provide a specific breakdown for annual gun murders, but Gunpolicy.Org website, an online database of gun statistics run by the University of Sydney, estimates 3.48 murders per 100,000 people in Thailand -- a ratio on par with the United States.
But Gunpolicy.Org puts the number at closer to 10 million after accounting for weapons purchased on the booming blackmarket.
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