Of the 120 seats in the New Zealand parliament, the incumbent conservative National Party won 56 seats, the center-left alliance of the Labour Party and the Green Party 54 seats, and New Zealand First nine seats.
The Green party said the results showed New Zealand was ready for a change of government.
New Zealand Prime Minister Bill English remains confident of forming government - despite the loss of the two seats.
Popular views believed Peters would choose National Party eventually, given the voters' say, though he started negotiations with both sides this week in an insouciant manner.
The extra Green seat means New Zealand will gets its first ever refugee MP.
Greens leader James Shaw said his party wanted to be at the heart of a three-way coalition and he had a "polite and cordial relationship" with Peters.
"I don't think it weakens it significantly at all", he said, referring to National's negotiating position.More news: GST Council to trim list of items in highest tax slab
More news: Dhawan returns as India opt to field
More news: Nigeria Vs Zambia Tickets Go For N1,000, N500
In New Zealand a party must reach 61 seats to hold the majority under the proportional representation system.
Winston Peters, the leader of the New Zealand First Party, has kept his cards close to his chest but told local media on Saturday that the release of the final vote count would put them in a better position to make decisions.
Why do Kiwis support NZ First?
Ardern said Labour would negotiate with the Greens and NZ First separately and not have all three around the table together.
He expected coalition negotiations to start "quite soon", as Peters has nominated a deadline of October 12, next Thursday, as the date by which he will choose which way to jump.
Ardern, meanwhile, highlighted that most electors had voted for change.
The National Party has held power for the past nine years. These may include plans to slash migration to 10,000 a year - a drop of more than 60,000; a ban on foreigners buying land, and establishment of a foreign ownership register; moving public service jobs out of Wellington to regional areas; holding a referendum on the anti-smacking law; and installing New Zealand woollen carpets in all government departments, schools and agencies.