The problem had affected about 4 percent of the network south of Taupo, Telecom chief executive Paul Reynolds said.
"We've improved overnight. It's now about 3 percent and it's fundamentally about Dunedin and the south," he told Radio New Zealand this morning.
"We've been working through the night over the past while, in fact progressively narrowing down the boxes in the network that are affected and rerouting things around them, bringing our customers back into service."
It was a problem with the hardware causing the faults, which technicians had to work around by rerouting customers, then removing the boxes to fix it, he said.
Mr Reynolds apologised for the disruption.
"The service given to customers -- particularly in Dunedin -- has been poor, but we have tried to keep in touch and bring things back as quickly as possible."
Telecom was working to get customers' phones working again one by one, but he could not give an estimate of when the problem would be fixed for everyone.
The issue of compensation would be addressed this afternoon, Mr Reynolds said.
The network crashed about 11am on Wednesday.
