The trade also means Northland, one of poorest regions in country, is missing out on jobs and income because swamp kauri is being processed overseas in countries such as Poland, the US and China.
The groups say they have repeatedly provided MPI and Customs with evidence of illegal exports but to their knowledge no action has been taken.
"We are left with the sense that MPI are either complicit in unlawful activity or totally inept at performing their statutory duties," the complaint's authors state.
The fact that the exports were not being picked up at the border suggested Customs was similarly implicated.
Evidence included online advertisements from overseas firms offering kauri logs that could not be exported legally. One company even documents the export of huge kauri logs on its website.
Fiona Furrell, chair of the Northland Environmental Protection Society, said a full-scale, independent inquiry was needed.
"We have irrefutable proof of the product [swamp kauri] offshore. It's getting there somehow. How that's happening is something MPI needs to answer," she said.
MPI forestry and land management director Aoife Martin said the Ministry was committed to enforcing the rules around swamp kauri exports and making sure exporters understood them.
"MPI will and does follow up on information from the public that suggests the rules are not being followed. This includes investigating numerous claims by the Northland Environmental Protection Society of illegal activities."
None of the recent allegations were new to MPI, Ms Martin said. In the specific cases raised by the society, MPI had "clear and robust" information that the exports were legal and that the Ministry's processes were working.
"The rules around what can and can't be exported have several layers to them and this appears to have lead to some public misunderstanding."
The actual extraction of swamp kauri, and its effect on the environment, was overseen by the Northland Regional Council, not MPI, she said.
A spokesman for the Office of the Auditor-General confirmed the complaint had been received. The office was looking into it.