Opposition parties say the visa fraud that allowed 231 Chinese students to get into New Zealand must be fully investigated.
Labour and New Zealand First are also calling for tighter rules around student visa applications following yesterday's revelation that agents in Beijing were behind fraudulent applications filed with Immigration New Zealand.
Authorities are asking the students to identify themselves and say they might not know they hold visas granted on the basis of falsified qualifications and bank statements.
Immigration New Zealand says 60 students are in the country unlawfully because their visas have expired and 171 have valid visas but could be liable for deportation depending on their circumstances.
A total 279 were involved in the scam but 48 have either left or haven't arrived yet.
The Government says the agents involved weren't accredited to Immigration NZ and Labour's export education spokesman Raymond Huo says that raises important questions.
"If they weren't accredited, why were their applications accepted in the first place," he said.
"The Government must make sure the rules around assessing qualifications and the visa process are robust so that only eligible and qualified students come here."
New Zealand First leader Winston Peters says the "bungling" is inexcusable and the Government must launch an inquiry.
Immigration New Zealand is investigating whether its own staff were involved.
Tertiary Education Minister Steven Joyce says "one or two" Chinese nationals hired by the department might have been.
NZN