The Green Party is pushing for all prisoners to be able to vote - not just those with sentences of less than three years.
The proposed law change, named the Electoral (Registration of Sentenced Prisoners) Amendment Bill, will allow prisoners with sentences of less than three years to vote in the general election.
It is currently in committee stage.
The party's justice spokesperson Golriz Ghahraman said the bill in its current form vote was a "great first step".
However, she added it "still means that a large number of people we hold in our prisons don’t have the basic human right of casting a vote during election, which our Supreme Court agrees is a serious breach".
"Prisoners are already carrying out their punishment by being in prison, she said. "Denying them basic human rights to access democracy only serves to further ostracise them from their community."
Ms Ghahraman said New Zealand's prison system "disproportionately targets Māori and other communities of colour, so this breach is also a serious race equity issue which we know has caused serious unrest internationally and here in New Zealand".
Last November, 1 NEWS exclusively reported the Government intended to reverse the blanket prisoner voting ban introduced by the then-National Government in 2010.
At the time, Justice Minister Andrew Little called it a "nasty little law that was not about the ability for prisoners to stop offending, it was just sort of a kick in the guts".
He also ruled out extending the voting rights to all prisoners, saying he accepted the "principal that when you go to prison you do lose some rights".
Mr Little's position has not changed, telling 1 NEWS today his role as Justice Minister was to "progress the bill as agreed by the Coalition Government".
"The (supplementary order paper - proposed change) is not a Government SOP and so we will not be supporting it."
NZ First's justice spokesperson Darroch Ball also said the party would not support the proposal.
The proposed law change is currently in the committee stage, having passed its first and second readings. It still needs to pass a third before it could become law.
National's Nick Smith said during the first reading there was a "huge irony that at the time the world is grappling with the crisis of the coronavirus, the Government is wanting to ram through Parliament, only six months out from an election, a bill to give prisoners the vote".
"Doesn't that speak volumes about the priorities of the Government?"
"If the Government really wanted to ensure that our electoral law was compliant with the Act, it would go the full hog, and it would be providing for all prisoners to be able to vote, and not just those sentenced less than three years."
If the bill passes in its current form, about 1900 prisoners would be able to vote at the 2020 election.
A 1 NEWS Colmar Brunton Poll found last October a slim majority of New Zealanders believed some prisoners should be allowed to vote.
A High Court ruling found National's 2010 amendment to the Electoral Act, disenfranchising prisoners, did breach the Bill of Rights. This was appealed to the Supreme Court.
In November 2018, the Supreme Court upheld the High Court's finding the blanket ban was inconsistent with the Bill of Rights.