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Mr Joyce has rejected the issue on the grounds the matter is not yet a serious problem.
Taxi Federation president Tim Reddish has responded by asking its member companies to provide examples of when private-hire operators are working as taxis.
Taxi companies moved to protect their business from private-hire operators in August.
This was shortly after legislation for compulsory security cameras and monitoring took effect.
However, despite fears their business may be poached by private-hire operators, there appears to be little evidence to back the federation's claims.
The Taxi industry magazine recently reported Mr Joyce had received advice there was no evidence the private-hire issue had become a "serious problem".
In a letter to Mr Reddish, Mr Joyce acknowledged concerns about the possibility of unfair and illegal competition from former taxi drivers operating under the guise of private hire.
New Zealand Transport Agency principal transport officer Dermot Harris said private-hire operators were not a major issue in the Otago-Southland region.
He said the agency had not received any complaints locally in relation to private-hire vehicles since August.
Most private-hire registrations in Otago-Southland were small business operators, Mr Harris said.
They offered tourism and limousine-style services, including for weddings and cruise-ship tours, he said.
The agency held regular discussions with taxi operators in the Otago-Southland region.
The issue of private-hire competition had been raised in the past, Mr Harris said.
"The relevant legislation and the limitations of private-hire service has been explained," he said.
"We have had no incidents reported to us that needed follow-up action."