Along with the two human trafficking charges, Islam, a 37-year-old company director, faces an additional 28 charges relating to the exploitation of five workers on temporary entry visas, the provision of false and misleading information to an immigration officer, aiding and abetting to breach visa conditions, and attempting to pervert the course of justice.
Ahmed, a 34-year-old accountant, faces a total of 14 charges for human trafficking, the exploitation of the five workers, providing false and misleading information to an immigration officer and aiding and abetting to breach visa conditions.
"We have decided not to further advance name suppression and today it will lapse. We accept that the public should know of this case," the couple told the Herald in a statement.
"What the charges really relate to are allegations that arise due to our involvement with a company that ran a small local retail shop and where some employees allege that they were underpaid or otherwise mistreated."
Both denied doing so, but accepted the new business struggled financially and was forced to close.
"However, it is our position that we acted at all times responsibly with all employees," they said.
"The only reason such charges, as those described as 'human trafficking charges', we believe are alleged in our case or in our view that we are charged at all, is because the employees concerned were on visas that allowed them to stay and work in this country.
"However, the fact that the relevant employees were on such visas is very relevant to this case and we will say is the motivation behind their allegations, which we deny. Without a current visa they would be required to leave. Because of the allegations, they have been permitted to stay and to work for another business."
Islam and Ahmed said the charges would be defended and both "remain confident that, after hearing all the relevant evidence, the court will correctly decide this case".
Trafficking in persons is punishable under the Crimes Act with imprisonment for up to 20 years, a fine of $500,000 or both.
The maximum penalty on the exploitation, false and misleading information and aiding and abetting charges is seven years' imprisonment and/or a fine up to $100,000.
While, the maximum penalty for attempting to pervert the course of justice is seven years' imprisonment.
The first people trafficking charges in New Zealand were brought by INZ in August 2015.
Two men were charged for arranging by deception the entry of Indian nationals into New Zealand. They were both found not guilty of the trafficking charges, but one was convicted on other charges.
The first person to be convicted of people trafficking in New Zealand, Faroz Ali, was sentenced in December 2016 to a total of nine years and six months in jail and ordered to pay a total of $28,167 reparation to his victims.