Social Development Minister Anne Tolley is willing to consider allowing the registration of child sex offenders to be reviewed after 15 years.
The Social Services Select Committee has made the recommendation in its report on a bill setting up such a register.
The initial proposal was for them to be placed on the register for life.
Under the bill, offenders, including those deported to New Zealand, would have to be listed on the register.
The Attorney-General has said that being on it for life could breach the Bill of Rights Act, as the punishment would possibly be disproportionate to the crime committed.
In the report, the committee said it hoped to ease those concerns by recommending that, after 15 years, those offenders would be allowed to appeal to be taken off the list indefinitely.
Mrs Tolley said she would consider the advice.
"Where you see registers around the world, they also have that ability to have a review," she said.
"I think it was a sensible suggestion, it's not one that I'm averse to, and I understand a judge would make that decision [whether they would be taken off the register]."
The 10-year cost of the register would be $146 million.
In the report, Labour Party MPs said the money could be spent on other proven strategies for curbing sexual offending, such as rehabilitation.
But Mrs Tolley said this was not an "either or" scenario but an "and and" scenario and anything that could be done to keep children safe was well worth doing.
In the past, there have been debates about whether the register should be made public but the committee has recommended that it only be available to approved agencies.
The register would only be available to some agencies including police, Corrections, Ministry of Social Development and Housing New Zealand.
New Zealand First's Darroch Ball said the public of New Zealand had the right to know.
"If we put the child at the centre of the discussion, which we should do, then the child has the right to know that their parents know where the child sex offenders are in the community," he said.
"We believe this register should not be viewed as a punishment for offenders but rather as a way to monitor sexual offenders in our communities."
But National, Labour and the Green Party were all strongly opposed to making the list public, saying evidence proves it could increase the risk of reoffending by severely disrupting the life of the abuser and their family.
The bill now goes back to the House for its second reading.