Ardern said Putin's decision to mobilise and issue broader threats was an "extraordinary escalation" of the conflict and called for a "rallying cry from the world" against Russia for its invasion of Ukraine.
"What you see in Ukraine is illegal, it is immoral. It is causing a loss of civilian life and that loss could extend if, as Putin has claimed, he expands the types of weapons used in this war," she said.
Zelensky's speech called for the punishment of Russia for its invasion. He called for a specialist UN tribunal to be established to investigate Russia's crimes in the invasion. He called Russia a "terrorist state".
Biden and Ardern made similar sounds on Ukraine.
In his own address to the General Assembly, Biden said that Putin made "irresponsible nuclear threats" and repeated a longstanding American position that a "nuclear war can not be won, and must never be fought".
Ardern may also find Biden an ally in a longstanding New Zealand frustration with the United Nations Security Council.
Since the founding of the UN, New Zealand has opposed the right of the five permanent members of the security council to wield a veto over resolutions.
While the United States, which is one of those five permanent members, is not proposing to ditch the veto, Biden suggested a willingness to reform the security council by increasing the number of seats on the council from 15 and adding new permanent members.
"We have long supported permanent seats for countries in Africa, Latin America and the Caribbean," Biden said.
The five permanent members are currently China, France, Russia, the United Kingdom and the US.
Russia has been accused of blocking progress on the security council with its veto - although the United States uses its veto powers from time to time as well.
Guterres has also spoken of the need to reform the UN for the future.