The quake was registered about 9pm on Friday, south of the Kermadecs, about 1000km northeast of the North Island of New Zealand.
"Based on current information, the initial assessment is that the earthquake is unlikely to have caused a tsunami that will pose a threat to New Zealand," the agency said.
"Detailed safety advice will come from local authorities and emergency services in the area. People should act on it promptly," the agency said on its website.
"The National Emergency Management Agency, local Civil Defence authorities and scientific advisors are closely monitoring the situation."
"Anyone near the coast who felt a LONG or STRONG quake should MOVE IMMEDIATELY to the nearest high ground, or as far inland as you can," the agency said on the social media platform X as a warning.
The US Geological Service is rating the quake at a 6.6 magnitude. It was initially measured at 7.0.
The Kermadec Islands are mostly uninhabited, except for a New Zealand monitoring station on Raoul Island.