Jacinda Ardern and Bill English are both claiming a mandate from voters after the results of the special votes were announced.
The special votes have evened up the two alternative governments, with National on 56 seats and the Labour-Green bloc on 54 - and both needing the nine votes of Peters' New Zealand First Party.
Despite losing ground, English said National was still 10 seats ahead of Labour, and also ahead of the Labour-Green Party bloc.
"Voters had a clear choice at the election between the two major parties that had a realistic prospect of leading the next government.
"They signalled very clearly that they wanted National to perform that role and we will now get on with the job of trying to give effect to their wishes.
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"It doesn't fundamentally change the equation. National is significantly the largest party...the fundamentals haven't altered."
English said the negotiations were much more likely to focus on the economy, than the number of seats held.
Watch: Bill English comments after final election result
English said he remained as determined as ever to lead the next government. Just half an hour earlier, Ardern told media she expects to be Prime Minister soon.
"These results show that the majority of New Zealanders voted against the status quo," Ardern said. "[They] voted for change. I would be proud to be a Prime Minister in a changed Government.
"We will continue our negotiations in earnest with potential support parties, beginning this weekend."
Winston Peters has said NZ First wants to have a decision made on who to support by this Thursday. Asked directly if she expected to be Prime Minister Ardern after those talks, Ardern said yes.
"That is what we are in these negotiations for. That's what we campaigned for. To be in a position to make change.
"I ran a strong campaign on behalf of Labour to be in the position to be Prime Minister, to lead New Zealand, and to improve the lot of all New Zealanders. That is what these negotiations are now about."
Peters told Newstalk ZB today there was no reason why his party could not make a decision by Thursday.
"It was always going to change and so the special votes were always important for that reason and knowing the facts now as we have them puts us in a better perspective to make judgments," Peters said.
He expected parallel talks with National and Labour to resume at Parliament tomorrow, subject to agreement.
"But it is not going to be a simple exercise.
"It is extraordinarily complex and you've got to have regard to every one of your colleagues and the member of your board's views," he said.
"But we can construct a serious comparison for them to look at when these talks are over and we should be able to come to a decision pretty promptly after that."
In Auckland, Ardern said she acknowledged there was now a need to get down to negotiating if the Thursday deadline was to be met.
"We are focused on making sure we can find resolution as quickly as possible. But we will do that responsibly. We will make sure that we take the time needed and try and strike the balance between moving quickly but moving responsibly."
Watch: Jacinda Ardern says Labour 'a bit closer to the number I wanted'
Peters has said his party is yet to decide on its preferred governing framework.
Possible options open to the party include a full coalition inside Cabinet, a support agreement offering confidence and supply in return for some ministerial posts outside Cabinet, to sitting on the cross benches offering support on case by case basis in return for minimal policy gains.
Ardern said she would be "proud" to lead a Government that was reliant on NZ First. Asked if she would be comfortable leading one where NZ First sat on the cross benches, she said her focus is on forming a "stable, durable coalition government".
"Beyond that, I'm certainly not going to reveal anything that happens behind closed doors."