Labour's immigration spokesperson Pete Hodgson has told Parliament threats were made against people at the centre of an immigration case involving a National Party MP.
Police have confirmed Kanwaljit Singh Bakshi, a first-term list MP, is being investigated for allegedly giving false job offers to Indians trying to get into New Zealand.
In 2008, an investigation by the Department of Immigration into the matter began but was closed due to insufficient evidence. New inquiries began when new information was provided in July.
Mr Hodgson has a legal statement given to police by Darshan Singh Suran who knows that Kuldip Singh paid $22,000 to an immigration consultant for what turned out to be a false job offer from Mr Bakshi.
Mr Suran says Mr Singh was threatened when he went public with his story.
Mr Hodgson used parliamentary privilege to read out the statement in the House on Wednesday, saying that "political people" contacted Mr Singh when his story was published and asked him politely to stop what he was saying.
The statement says when he refused, they started to threaten him.
Up to authorities to investigate - English
Outside the House, Deputy Prime Minister Bill English said it is up to authorities to investigate the allegations.
Mr English said Prime Minister John Key has always said any allegations against Mr Bakshi should be put in front of the appropriate authorities, and he should be treated like anyone else.
"There's been allegations around for a while. It's my understanding that the Department of Immigration has been looking into those and they should follow the proper processes."
Mr English said Mr Bakshi has been clear that he has not done anything wrong.
A police spokesperson says they are unsure how Mr Bakshi is involved in the allegations and investigations have been widened to look at his role.
The spokesperson says the main target of the investigation is the immigration consultant and it is not clear what Mr Bakshi's role was.
Mr Bakshi could not be reached for comment. He is on sick leave and recovering at home after a heart bypass.