"We understand he has made an appeal to the minister and therefore cannot comment further at this time."
Singh made his first refugee claim two weeks after he arrived with the help of Kulwant Singh, a man who was last year jailed for 25 months for arranging false refugee applications.
Kulwant Singh was described in court at the time as a man who "cooks up" stories about Indian workers being violently treated so they could gain refugee status.
When Amarjit Singh's claim was denied he took on a fake identity, grew a beard and wore a turban for new passport photos.
With the help of Kulwant Singh, a second refugee application was made under his new identity.
This was also declined August 2001, as was his appeal in June 2002.
Over that time however, Singh formed a relationship with a Maori woman. They had twin boys in December 2001, and a daughter in 2003.
Their relationship ended after their youngest daughter was born in 2011.
His lawyer Kamil Lakshman said the children, all New Zealand citizens, were "vulnerable, scared and lost".
"They don't know what is going to happen to their father, and underlying this is the question what is going to happen to them," Lakshman said.
"Their father has been the constant figure in the entirety of their young lives."
Lakshman claims Amarjit Singh was a "victim" and had taken on the fake identity and lodged fake statements to Immigration under the advice of Kulwant Singh.
"It make no sense to deport Mr Singh as his contribution to the three New Zealand-born children are greater as his presence avoids their displacement, destruction and dependency on the state," Lakshman said.
In a submission to the minister, the lawyer argued that public policy reasons outweighed Singh's deportation in this case.
He has custody of three children, Lakshman said, and they faced a bleak future if he was deported.
It was not possible for the children to return home with Singh to his home village of Rajpura.
"Given that Mr Singh has a high-needs child, this will be as good as a death sentence for him," she said.
Singh's children have been writing letters to him in prison since he was taken in three weeks ago.
Son Ranbir, 15, who is due to have orthopaedics surgery on Friday, said he wanted his father home.
"I have surgery...for my hips and I wouldn't be able to go by myself without him there with me," Ranbir said.
"Since my dad was taken...my life has been hard, and it has been hard for me to focus at school and everything else."