Most users' connections would "self-restore" but failures may recur after a period of time. Some customers may need to turn off and restart their modems to enable reconnection.
Telecom apologised for the inconvenience to affected customers.
"We understand how important your broadband service is and resolving service for all our customers is our primary focus at this time."
The issue has strained the company's call centre, which this morning was experiencing "higher than normal levels of calls for this time of the day".
"If you're waiting on hold with us, sorry - we currently have high call volumes," Telecom said in a tweet.
Today's issue comes after Telecom said it would review its broadband system after two massive outages yesterday. It also follows an outage less than a fortnight ago, in late November.
Hundreds of thousands of customers nationwide were without broadband last night after an outage about 9.45pm yesterday.
Telecom said technicians restored the affected server about 11.35pm.
Earlier yesterday, some 300,000 broadband customers - roughly two-thirds of Telecom's broadband customers - lost services after a problem arose during a software upgrade.
Telecom said the problem with parallel servers in Auckland and Christchurch meant customers' modems were failing to authenticate when trying to communicate with the server.
Many customers' internet access had reconnected automatically, but Telecom said some people would need to reboot their modems to get back up and running.
Telecom retail chief executive Chris Quin said it was urgently investigating why yesterday's issues occurred.
"We have a comprehensive review underway to ascertain how these issues can be minimised in the future and apologise unreservedly to customers for any disruption these outages caused in the interim," he said.
On November 30, about 25,000 mainly residential customers lost service lost their connections after a fibre-optic cable failed after system upgrade work.
Telecom at the time apologised for the inconvenience - but ruled out compensation for customers who lost productivity due to the outage.