Those under SFO investigation last year were Te Wananga o Awanuiarangi, Manaakitanga Aotearoa Charitable Trust and Taratahi Agricultural Training Centre.
Mr Cunliffe said Labour has also had a response to an Official Information Act (OIA) request that showed 35 tertiary providers had "widespread or serious" educational delivery issues.
Those named included the three under SFO investigation, plus First Aid Specialists Ltd, Te Wananga o Aotearoa, Victoria Institute (NZ) Ltd and the Western Institute of Technology, Mr Cunliffe said.
NZQA had withheld 27 of the names in Labour's OIA response due to commercial reasons, which Mr Cunliffe said was not transparent enough.
He called the issue "systemic".
"Our international education reputation is now in serious trouble. It is clear there is something very wrong with the way our tertiary institutions are run," Mr Cunliffe said.
"Steven Joyce now has to act. As a first step to cleaning up this sorry mess, he must name the other providers at the centre of these latest investigations. Students and staff cannot be left in the lurch by his failure to act."
Minister for Tertiary Education, Skills and Employment, Steven Joyce, said the SFO activity in the tertiary sector demonstrated the robust approach that the TEC takes to the oversight of the sector.
"It's important to note that the SFO describes its own activity in relation to Intueri as 'making inquiries' rather than as an investigation," he said.
"We won't be making any comment about other individual institutions as the SFO may find that no laws have been broken, and they also may find that to be the case with Intueri."
He described Mr Cunliffe's accusations as "breathless" and said the vast majority of tertiary institutions do a great job.
Intueri chief executive Rob Facer said it had announced to the market on Friday that it had been approached by the Serious Fraud Office. The Office was undertaking an inquiry under Part I of the SFO Act, he said.Intueri was complying in full, he said.
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• The $25 million student funding scandal
The Story So Far
TE WHARE WANANGA O AWANUIARANGI: October 2014
The Whakatane-based wananga agrees to repay $5.9 million in taxpayer funding after an investigation finds New Zealand Warriors players and staff gained qualifications after doing one day of an 18-week tourism course. Volunteers at a national kapa haka festival also received certificates. Donna Grant, Awanuiarangi's director of performing arts, resigns from the wananga and is referred to the Serious Fraud Office.
WITT: November 2014
Six staff members resign as the Western Institute of Technology in Taranaki repays TEC more than $3.5 million following an investigation into its National Certificate in Maori Performing Arts courses. A probe by forensic accounting firm Deloitte found students were not properly enrolled, attendance records were poorly kept and qualifications granted without assessments.
TARATAHI: September 2015
Masterton's Taratahi Agricultural Training Centre agrees to repay $7,549,000 it received over a six-year period during which it overcharged the taxpayer. A second breach involved enrolling 67 staff in an entry-level programme when little or no teaching took place. Taratahi's former chief executive, Dr Donovan Wearing, died suddenly in January, three months after the TEC confirmed it was undertaking a "targeted review" of the organisation. A second SFO investigation is launched.
AGRIBUSUSINESS TRAINING: October 2015
Agricultural training provider Agribusiness Training Ltd collapses after being ordered to pay back $6 million in taxpayer funding for under-delivering contracted teaching hours. Deloitte found five Agribusiness programmes delivered fewer teaching hours than its NZQA programme approvals specified.
MANAAKITANGA AOTEAROA CHARITBLE TRUST: November 2015
Rotorua private training establishment Manaakitanga Aotearoa Charitable Trust is stripped of its NZQA registration and ordered to repay $2.6 million in TEC funding. Operated by Donna Grant, the Maori performing arts college is subjected to reviews by Deloitte and NZQA, which find it under-delivered teaching hours, failed to record student attendances and over-reported the number of students successfully completing their studies.