People trying to reach emergency services on Saturday had their calls go unanswered and were eventually cut off.
Emergency 111 calls are answered by Spark Communications, then forwarded to the appropriate emergency service.
Company spokesperson Richard Llewellyn said the problem happened because of an unusually high number of calls to the emergency number between 12:10pm and 12:20pm on Saturday.
St John Ambulance said there were a high number of emergency calls on Saturday.
The police said a call by a Wellington woman which was dropped was not due to a lack of staff. She called 111 at midday on Saturday, but police said that her call had been dropped when it was transferred from the Spark call centre to them.
Police said they believed the problem was a network issue involving her 2Degrees phone service and Spark.
A Spark report from midday on Saturday showed there were 71 calls at the time of the dropped call, including 29 for the Police, and 17 for the Ambulance service.
St John assistant operator director Neil Lilley said the higher than usual call volume on Saturday was a one-off and they did not have difficulty with people struggling to reach their call centre.
He said there were usually no problems at all with the Spark service.