Police say it is unacceptable that the 111 system failed in the early hours of Sunday morning, affecting calls at a peak time for emergencies.
The national fault stopped people reaching emergency services early yesterday.
Those trying to get through between 12am and 12.45am received an automated message saying the system was overloaded.
Although a backup system took effect, the queue of calls took up to 40 minutes to clear, before the main 111 system was restored at 2am.
Inspector Mal Schwartfeger told Morning Report it was a software fault and the police were assessing how many people tried to get through.
He said Saturday night was one of their busiest periods, with calls peaking at about 2am on Sunday mornings.
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He said some of the callers were ringing back on "numerous occasions".
In a statement released yesterday, police said it was an internal problem, and not an issue with the telecommunications provider Spark.
"We apologise to those people who were unable to access emergency services and can assure people that the system has been restored to normal service.
"We believe a number of callers were affected, however more work needs to be done before we know the exact number. We do know that some callers called back on numerous occasions"