Under present law, individuals, including gays and lesbians, can adopt children, but because of the way the outdated Adoption Act is worded they can't if they are part of an unmarried couple.
Green MP Metiria Turei recently placed a member's bill into the ballot seeking to extend adoption rights to those in civil union and de facto partnerships.
Most member's bills placed in the ballot are not drawn and never get a chance to be debated.
Justice Minister Mark Burton said at the time he was "not unsympathetic" to the bill and would give it careful consideration if drawn.
Mr Carter, a gay MP, expressed his support for the bill in the Weekend Herald and when asked yesterday why the Government wasn't introducing such a bill itself, he said: "The Government hasn't decided yet whether it's not doing it itself. We're still talking about that.
"The private member's bill has of course focused the Government's attention on the issue. I'm not the Minister of Justice so I wouldn't be prepared to say what we're doing, but I can confirm as a Cabinet minister that we are thinking about the issue seriously.
"I've expressed a view as an individual that the Kahui twins showed us once again that it's actually about the quality of individuals who are caregivers, not about their sexuality or their marital status.
"Speaking as a gay individual, not as a member of the Cabinet or the Government, it is important because of equality.
"I know that there are a lot of gay and lesbian couples who make excellent parents, they're fine and decent people who could offer a lot for a child and they shouldn't be denied that opportunity.
"The reality is that lots of gay people do have children. I myself have children. All the research has shown that the sexuality of a child is not determined by the sexuality of a parent.
"So to say that adopted children will become gay because they're adopted by gay parents is absurd."
Ms Turei welcomed the news the Government might adopt her bill, saying it was preferable to pinning her hopes on the ballot.
It would be a "great way" of marking the 20th anniversary of homosexual law reform, she said.
"They did avoid the issue during the civil union debate when it should have happened."
The Relationships (Statutory References) Act passed with the civil union law changed about 100 pieces of legislation to ensure equal rights for civil union and de facto couples.
"But the Adoption Act was purposefully left out because I think they considered it too politically sensitive to deal with."
This had been "foolish" because it would have been easier to do it then, than court a renewed furore by treating it separately, she said.
Many critics of the proposal failed to understand the existing law and their arguments were therefore often irrelevant, she said.
"A single gay guy can adopt, a single lesbian can adopt. So anybody who tries to argue that because they're gay, or because they're not in a loving heterosexual marriage [they shouldn't be able to adopt], those people don't understand the law because you don't have to be in a loving heterosexual marriage to adopt."
The law was effectively silent about the sexuality of single parents.
"But because it's worded in a very old way it only talks about husbands and wives when it's talking about couples so it means that a gay and lesbian couple cannot legally adopt."
Mr Burton could not be reached for comment yesterday.