National leader Bill English is looking to stitch up a deal to govern with Winston Peters fairly quickly.
Speaking to media on Sunday English said the public wanted a strong government formed with some haste.
Labour leader Jacinda Ardern, who could also form a Government with Peters' NZ First Party and the Greens, has indicated that she would like to wait until the special vote is counted on October 7.
Both leaders are travelling to Wellington on Monday. Neither has talked to Peters yet, although English said his staff were in the process of setting up a phone call.
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"We want to get on with the job of forming the Government, but we will work with NZ First at the pace they are willing to go, and as Mr Peters has indicated he also wants to move at a pace that respects the public's desire to get the issues dealt with and get a government formed," English said.
"Our position going into those is almost one in two New Zealanders supported National and the voters have given us the task of forming a government with NZ First."
English refused to discuss negotiating positions with the media but said keeping the economy strong would be key.
He was open to several possible governing arrangements, including a formal coalition, a confidence and supply deal, and an "abstention" deal where Peters agreed to not to vote on confidence votes.
English said it was not necessary to wait for the special vote.
"It's possible that a couple of seats could change hands but it's not going to alter the current balance much," English said.
The special vote - bringing together overseas votes and people who enrolled during the early voting period - will make up about 15 per cent of the total vote, or 384,072 votes.
It is expected to give one or two seats to the left bloc, giving them a stronger hand in coalition deals.
Currently a Labour-Green-NZ First deal would only just scrape up to the 61-seat governing line, while a National-NZ First deal would provide a comfortable 67 seat arrangement.
Ardern said earlier it would be easier to wait for the special votes but talks could begin before then.
"It's hard to go too far without know that remaining 15 per cent," Ardern said.
"At this time parties are wanting a little extra time to considering their position and to consider the special votes.
"It's making sure that everyone's vote has been counted before we start forming a Government."
"Of course we are here ready to have those conversations."
Green Party leader James Shaw said he expected Labour to lead the negotiations.
"I would completely expect Labour to take the lead in negotiations and I expect have one-to-one conversations," Shaw said.
Peters himself is not giving much away.
"Nobody quite knows what the [election] result last night means," Peters told reporters in Russell on Sunday morning.
He said special votes could change things "marginally".
"In the meantime we've just got to wait and see what that means, and talk to my colleagues over the next few days and then we'll tell you what we're going to be prepared to do."
"We know what we've got to do responsibly. We're going to talk as a political party, as a caucus and as a board, and when we've made our decision we'll then start talking to other people about what we might do."
He also declined to discuss negotiating positions or bottom lines with the media.
English said the ACT Party was not likely to be part of a National-NZ First coalition.
He wouldn't comment on whether or not he would resign should National end up in opposition, saying there was no way that was going to happen.