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.