Justice Minister Amy Adams says quashing pre-1986 convictions for sex between men could require case-by-case investigation and may prove to be too difficult.
To mark the 30th anniversary of homosexual law reform, Green MP Kevin Hague tabled a petition in Parliament today in the name of Wiremu Demchick, signed by 2100 people.
The petition requested that Parliament issue an official apology to those convicted of consensual homosexual acts before legalisation in 1986.
It also requested a law change which set out a process for reversing the convictions.
Ms Adams said today that she would wait for a select committee to consider the petition before any decision was made about an apology.
She warned that reversing convictions would be a hugely complicated task.
"It's a very difficult process actually because the way the law is crafted it didn't distinguish between consensual and non-consensual acts.
"A lot of the offences are still offences under today's law around under-age children and the like, so it's not as simple as a blanket approach.
"What we've identified is that it would take quite a detailed process if it was even possible to go through case-by-case and work through whether each offence in each case would still be illegal under today's law."
The total number of convictions is not known, though Mr Hague said it was believed to be "in the hundreds".
Ms Adams she she had been advised that 80 per cent of the convictions would still be offences under today's law.
She was not aware of a precedent for a complete reversal of every conviction under a specific law.
Mr Hague pointed to the case of Bastion Point activists, some of whom had their charges quashed.
He said a tribunal could be established to investigate each case.
The convictions blighted the lives of many people, he said, and the Government was obliged to do what it could to put things right.
"Nobody, anywhere, at any time, should be expected to obey a law that offends against basic human rights.
"People who were convicted under historic immoral laws should not have to live with those convictions on their records today.
"It might seem like a lifetime ago, but I remember what living under this law was like, and many people still live with this hanging over their head."
Mr Demchick, the organiser of the petition, said his campaign was about recognising the trauma that the convictions caused, rather than preventing discrimination.
"This is more about recognising past wrongs. It wouldn't have a huge legal effect. As far as I know, no one is being kept out of a job or anything like that."
He said some people might be concerned about the precedent of retrospectively quashing convictions.
But he believed that his petition was a special case because public support for reversing the convictions was near-unanimous.