Mr McCully said New Zealand would work with other Security Council members on "an appropriate response" to the launch.
North Korea defied international warnings and launched a long-range rocket that the United Nations and others call a cover for a banned test of technology for a missile that could strike the US mainland.
The rocket, fired from North Korea's west coast and tracked by the governments in South Korea and Japan, came about two hours after an eight-day launch window opened this morning.
It follows North Korea's widely disputed claim last month to have tested a hydrogen bomb.
Washington, Seoul and their allies will consider it a further provocation and will push for more tough sanctions in the United Nations.
A South Korean defence official, speaking on condition of anonymity because of office rules, said the launch from the North's west coast launching pad was made between 9:30am and 9:35am local time, but gave no other details.
The Japanese government says no rocket debris fell on the Japanese territory and there are no reports of damage. Japan's NHK broadcaster reported that the Japanese government said the rocket passed over the southern Japanese island of Okinawa but no anti-missiles were fired.
North Korean rocket and nuclear tests are seen as crucial steps toward the North's ultimate goal of a nuclear armed long-range missile arsenal.
North Korea under leader Kim Jong Un has pledged to bolster its nuclear arsenal unless Washington scraps what Pyongyang calls a hostile policy meant to collapse Kim's government.
New Zealand joined other countries in quickly condemning the launch.
Japanese Prime Minister Shinzo Abe called the North Korean rocket launch and the recent nuclear test violations of UN agreements.
"Cully," he told reporters at the prime minister's residence. "We will take action to totally protect the safety and well-being of our people."
