The Opposition is calling on the Finance Minister to specifically rule out any move to cap rent rises.
Property investors - who say they feel attacked as a result of the housing reforms unveiled last week - are predicting rent hikes could soon follow.
Debate about the impact of the new housing package continues unabated.
Finance Minister Grant Robertson said the government would be keeping a close eye on any increase to rents and would "take action if necessary".
He unveiled a plan to dampen the overheated housing market] last week, which included tax measures directly targeting investors.
However, Prime Minister Jacinda Ardern is playing down the prospect of government intervention.
"We've got no further plans at this stage around the areas of rent," she said at Monday's post-Cabinet media briefing.
"I've seen a lot of speculation around what our housing package may mean for rents, but it is speculation, and so at this stage no further plans."
Any future action in response to excessive increases would be "hypothetical", Ardern said.
"When we saw increases in house prices, we then responded to that, but at this stage, it is speculative".
"What we've seen in our rental market has not mirrored what we've seen with house price growth," she said.
"In fact, more often than not, it's tended to mirror wage growth and so we will keep an eye on the numbers closely, but at this stage, we have no further plans in that area."
Eligible houses bought from last Saturday are subject to the extended 10-year bright-line test, and from October the ability to claim against mortgage interest will be removed.
For landlords who owned their properties before Saturday, there'll be a four year phase-out period for the deductibility change. New builds are exempt from both policies.
Robertson said a number of factors drove rental prices, including supply and ability to pay.
"The impact on rental prices is complex and uncertain. Any estimates at the moment are purely speculative. There are a number of factors in what makes up a rental price, including the supply of properties and people's ability to pay. We will consult on the detail of these proposals with the changes to apply from 1 October this year."
Stats NZ recorded a 3 percent increase to rental prices in the year to February, he said, but the government would monitor the ongoing impact of the housing plan, and "take action if necessary".
"I am fully aware that the current housing market has made life difficult for some renters, and finding new affordable rentals can be difficult," Robertson said.
"The government has put in place measures to support tenants to have more secure access to affordable, warm and dry rental properties, and we will continue to support renters."
"Tenants can also go to the Tenancy Tribunal if they think their rent is too expensive and not in line with the market, to request a rent reduction."
Under the law, landlords can only increase the rent once a year, and have to give tenants a set period notice. The law does not put a limit on how much rent can be increased by, but does direct it be done in a certain way, and lays out tenants' options if they disagree with the increase.
Calls for government to rule out any form of rent control - opposition
In media interviews over the weekend, Robertson did not rule out caps on rent hikes, telling Newshub Nation that while it wasn't "on the agenda, [they would] keep an eye on what happens".
He also said it was not on the agenda because he did not believe rents would spike.
Regardless, National leader Judith Collins said "the government should have ruled out absolutely any suggestion of rent controls".
They had been tried in the past elsewhere, she said, and had been "an absolute disaster and have led to massive shortages of rental properties".
The government needed to deal with the supply side and "stop making the markets incredibly nervous around the chopping and changing of policies and the attacks on landlords".
She acknowledged the challenge facing many renters, but said rent caps were not the circuit breaker needed.
What was needed was for the government "to stop demonising landlords and making it harder and harder for people to be a landlord".
"Every time the rents have gone up under this government there is one place that people should be looking and that is at the government - we told them that when they made the changes to the Residential Tenancy Act ... that they would lead to increases.
"Rents have gone up $125 on average in four years. That is absolutely at the foot of the government," said Collins.
ACT housing spokesperson Brooke van Velden said "when the property sector needs confidence to build, Grant Robertson has dropped another bombshell on property investors".
Robertson not ruling rent caps out "fuels a rocket of uncertainty", she said.
"Building housing supply is a long-term activity. Building homes takes years, paying for them takes decades. When the government changes the rules of the game at a whim, confidence suffers and less gets built.
"Developers are already reporting that they are pulling back while the market digests the latest policy changes, this is the cost of uncertainty, a cost on top of the actual policies announced," said van Velden.