The Fire Service in Christchurch said it did not have enough resources to attend all the earthquake-related callouts.
Numerous people were trapped following the devastating 6.3-magnitude quake on Tuesday.
The Fire Service said all its resources were committed and they were unable to get to some people because of damaged roads and bridges.
However, people who were injured or trapped were advised to keep calling the emergency 111 number.
Fire crews cordoned off the centre of the city because gridlock was hampering the rescue effort.
They were finding it difficult to fight the earliest fires because of limited availability of water, and monsoon buckets were being used.
Helicopters were used to rescue people from high buildings and extra fire-fighting appliances were sent from Timaru.