"We now have got a global momentum into lowering emissions in this great world that we live in and I think it is going to be decades of work.
"In that context there probably is room for some cross-party [discussion].
"I still think that there will be a number of differences between the parties. But I do think it's worth opening the dialogue and seeing if there's a few agreements we can come to."
A change to New Zealand's emissions reduction target - 11 per cent below 1990 levels by 2030 - is off the table.
Some Opposition parties and climate scientists say the target should be 40 per cent below 1990 levels.
Bennett said the existing target would already cost the economy between $14 billion and $36 billion.
"We better think about how we meet our target before we even think about being more ambitious."
But the minister said she was open to other changes as a result of discussions with Opposition parties.
This included alterations to the Emissions Trading Scheme, which is currently being reviewed.
She reiterated that there are no plans to bring agriculture back into the scheme, which requires industry to cover the costs of atmosphere-warming emissions.
Agriculture makes up 48 per cent of New Zealand's emissions.
Instead of bringing it into the ETS, the Government is investing in science and technology which could lower farming emissions.
"Certainly from what I have seen and heard from the scientists is they think there will be a breakthrough, a significant lowering of emissions through the use of technology," Bennett said.
Green Party co-leader James Shaw said the talk of a bipartisan approach was in its early stages, but it was a positive step.
"We'll have to wait and see, but I am really pleased that they are at least open to the possibility of cross-party dialogue because they have not been in the past."
Shaw said the decision to sign off the Paris Agreement was also "quite significant" because it locked in a target which had been until now been conditional.
"Essentially the Government has reversed itself and said, well actually, we will ratify and remove the conditionality.
"That means our target will become firm regardless of what happens in the international carbon markets.
"I think the target is weak. But the fact that we've ratified it is quite a big step."
Labour's climate spokeswoman Megan Woods also welcomed the Government's cross-party proposal.
She said it could help set clear rules for achieving New Zealand's target over the following decades, during which governments will change several times.
The Paris Agreement covers all countries' emissions targets for the 2020-2030 period.