"A politically exposed person is an individual who has been entrusted with a prominent public function, whether in New Zealand or abroad."
The FMA required Fullerton to implement a number of measures including a risk assessment; a compliance programme; review its "customer onboarding programme"; review all previous customer interactions; and improve its transaction monitoring rules.
It also said that Fullerton must check whether any of its customers were a politically exposed person, "using an internationally recognised search tool".
FMA director of regulation Liam Mason said the authority provided guidance and assistance to help companies to comply with regulations.
"We know that reporting entities have invested significantly in systems and resources to comply with the requirements of the law," he said.
"It's not fair on those who have made this effort if others do not do so. The FMA signalled in our last annual report that we would take formal action where we see firms failing to meet these requirements."
If Fullerton failed to the required actions the FMA would consider the need for further regulatory responses. This could include civil action, which can lead to penalties of up to $2 million per offence for a company.
Fullerton sells itself as "Asia's fastest growing brokerage firm".
"Our company is headed by Mario Singh, one of Asia's top thinkers and influencers in the online trading industry," it says on the Fullerton's Facebook page.
"As a world-class coach, Mario has been brought in by some of the biggest banks in the world to speak to their traders and clients. Some of his clientele include ICBC - China's biggest bank, Julius Baer - the third largest Swiss bank and OCBC – ranked by Bloomberg as the world's strongest bank in 2011 and 2012."
You can read the FMA's full warning here.
Fullerton could immediately be reached for comment.