Prime Minister Jacinda Ardern briefly met with the US President at his reception for world leaders attending the United Nations.
Before they posed for a photo together, Ms Ardern had a brief conversation with Mr Trump.
He congratulated her on the birth of her daughter Neve, and she acknowledged the work the president was is doing on the Korean Peninsula.
The prime minister also used the opportunity to promote the work of New Zealand and US officials on the lifting of steel and aluminium tariffs.
Ms Ardern and Donald Trump were in the UN General Assembly as the general debate got underway though their paths did not cross.
Earlier this week Ms Ardern said New Zealand would not be signing up to a US call for global action on the war on drugs, and preferred to take a health approach.
Ms Ardern remained expressionless during Donald Trump's half-hour speech this morning in which he lashed out at Iran.
He told world leaders that the regime in Iran was corrupt and its leaders sowed chaos, death and destruction.
"They do not respect their neighbours or borders, or the sovereign rights of nations, instead Iran's leaders plunder the nation's resources to enrich themselves, and to spread mayhem across the Middle East and far beyond."
Donald Trump said the US planned to impose further sanctions on Iran and called on all nations that import Iranian crude oil to cut their purchases substantially.
Mr Trump's speech continued his direction of taking making the United States more inward-looking, and promoting patriotism over globalism.
He also said the US would provide no support or recognition to the International Criminal Court.
"As far as America is concerned the ICC has no jurisdiction, no legitimacy and no authority."
Mr Trump also said his country would reconsider all of its foreign aid.
"The United States is the greatest giver in the world, by far, of foreign aid, but few if anything give anything to us, that is why we are taking a hard look at US foreign assistance.
"Moving forward we are only going to give foreign aid to those who respect us and frankly are our friends."
This article was originally published by RNZ.