A group representing migrant workers says 10 Chinese men found working illegally at Auckland construction sites should not be deported.

Two were due to be deported last night, but RNZ has not had official confirmation that the deportation went ahead.

The other men are being held in Mt Eden Prison until a date is set for their removal from the country.

Their lawyer, Matt Robson, said the workers were victims of human trafficking and paid substantial sums to a third party, who arranged travel and work.

Migrant Workers Association president Anu Kaloti said keeping the men in the country would help in investigating the case.

"I'm very confident that both workers can be extremely helpful in the investigation to expose the exploiting employers.

"People don't just bump into work and start working - they have been provided work by the employers.

"The culprits here are the exploiting employers, not the Chinese workers themselves."

New Zealand had "systemic, wide-spread" immigrant labour exploitation issues, Kaloti said.

"The minimum that this government can do is stop the practice of catching reserves of migrant workers to employers because that is bondage, that is akin to modern slavery."

Green MP Ricardo Menendez-March has called for the deportations to be paused to allow an investigation into the claims of migrant exploitation and human trafficking.

However, Minister of Immigration Kris Faafoi said he had been assured the proper processes were followed and Immigration NZ had not found any evidence of trafficking.

"Agencies are satisfied further investigations around employment and immigration breaches can be carried out without the need for the men to remain in New Zealand," Faafoi said.