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Someone purporting to Dr Clark on Instagram this morning messaged an Otago Daily Times reporter about an opportunity to take part in a "United nation development program".
The account appears to be a replica of Dr Clark's real account and contains images he has shared on his real account.
The real account is called davidclarkmp, with the fake account called davidclark_mp.
Dr Clark said he was checking on the situation, but was almost certain the account was not his.
It comes after Prime Minister Jacinda Ardern dismissed speculation on social media that the Government is poised to announce a total lockdown across the country to combat coronavirus.
"We will share with you the most up-to-date information daily. You can trust us as a source of that information," Ardern told reporters in Rotorua this afternoon.
"Do feel free to visit covid19.govt.nz - otherwise dismiss anything else. We will continue to be your single source of truth.
"Everything else you see, a grain of salt."
Ardern said that misinformation only fuelled public panic.
"When you see those messages, remember that unless you hear it from us, it is not the truth. New Zealanders must prepare, but do not panic."
- With NZ Herald