Prime Minister Jacinda Ardern made the announcement after meeting with Tongan Prime Minister 'Akilisi Pohiva in the capital Nuku'alofa this morning.
New Zealand has so far contributed $2 million of emergency relief to three Pacific countries hit by the cyclone - Samoa, Tonga and Fiji, $750,000 of which went to Tonga.
Ms Ardern arrived at the meeting in the Tongan capital Nuku'alofa with Foreign Minister Winston Peters.
Mr Pōhiva was flanked by his Finance Minister, Energy Minister, Health Minister, and Agriculture Minister.
He has taken time off due to ill health but appeared in fine form if a little impatient, consulting his notes and officials.
Climate Change Minister James Shaw and Social Development Minister Carmel Sepuloni had place tags but did not arrive with Ms Ardern.
Both Prime Ministers shook hands and exchanged gifts.
Mr Pōhiva presented Ms Ardern with a traditional wooden carving of a small Tongan house.
"It's beautiful," Ms Ardern said.
She then presented Mr Pōhiva with a piece of pounamu, noting that it can only be gifted.
The meeting took place in the Saint George Palace, named for a former king and built with $15.7 million of Chinese grant money. It was completed last year and houses the Prime Minister and several cabinet ministers.