Civil Defence's response to the 7.1 magnitude quake will be reviewed following criticism it was too slow to alert people of potential danger.
The Ministry of Civil Defence and Emergency Management sent out its first national advisory about the quake at 5.10am - about 40 minutes after the quake hit.
A potential tsunami threat notice was not issued until 5.33am and a request for an emergency announcement to broadcast was not made until 5.58am.
WeatherWatch head analyst Philip Duncan believed Civil Defence's response time was well below international standards.
"When the ministry [of Civil Defence and Emergency Management] puts out alerts and information, it's really detailed and informative, which is great, but it's far too slow.
"The first notification of the earthquake didn't come until 40 minutes after it had happened, then the tsunami warning came much longer after that.
"In that time, lots of people were becoming anxious and worried, not knowing what was happening."
Duncan said Civil Defence needed to put out alerts faster or the responsibility should be passed to GeoNet.
Minister for Civil Defence Nikki Kaye said the ministry would review its response to the quake.
"After any major event we look at potential lessons learned, and this will happen following [yesterday's] event," she said.
"[The ministry] has a project underway looking at current processes for national warnings and public alerting, and this includes looking at the timeliness of alerts.
"Any potential changes to current processes will be considered as part of this project."
Ministry of Civil Defence and Emergency Management director Sarah Stuart-Black said this morning's earthquakes did not meet the threshold for automatic issuing of a potential tsunami threat.
"The Pacific Tsunami Warning Centre indicated that there was no tsunami threat in their initial assessment.
"Twenty three minutes later at 5:33 the Ministry of Civil Defence & Emergency Management issued the national advisory for a potential tsunami threat in order to be proactive for public safety while we were still awaiting confirmation from scientists ...
"Today's tsunami was a local source event. This means that we have very little time to issue official warnings."
Stuart-Black rejected criticisms the ministry's response was too slow.
"We have a well-established and tested system that pulls together all the required experts when we need them, this includes the New Zealand tsunami experts panel, GNS Science and GeoNet."
People needed to know the natural warning signs of tsunami and take appropriate action, she said.
"If you are at the coast and you feel a strong earthquake that makes it hard to stand up, or a weak rolling earthquake that lasts a minute or more, move immediately to the nearest high ground, or as far inland as you can."