Thai media reported the pair, Hamish Day, 36, and Oscar Day, 38, were on motorcycles in a residential area in Phuket on Saturday, and failed to stop for a police officer who thought they were speeding and failing to stay left.
When they did eventually stop, the Bangkok Post reported they started shouting, and the officer used his phone to record them. The Kiwi pair then allegedly attacked him, trying to wrest control of his phone and pistol, which fired one round without hitting anyone.
More officers eventually arrived and arrested the Days, who then allegedly offered a bribe - which was turned down.
Both have been charged with physical attack against a policeman, bribery, robbery, obstruction of police duty and driving without a licence, the Bangkok Post said. They were expected to appear in Phuket Provincial Court on Monday.
"The Day family is understandably distraught over the situation with their sons in Thailand," their parents said Laurence and Katrina Day in a statement on Monday.
"We know very little more than has been reported in the press. We request privacy and your prayers while we try to deal with the situation."
The officer Hamish and Oscar allegedly attacked was injured, but treated and discharged from hospital. Chalong station chief Pol Col Ekarat Plaiduang said the officer they attacked would be "honoured and rewarded for his work".
The Ministry of Foreign Affairs and Trade has been approached for comment.
